diff --git a/cmd/testgen/main.go b/cmd/testgen/main.go
new file mode 100644
index 00000000..680c38ac
--- /dev/null
+++ b/cmd/testgen/main.go
@@ -0,0 +1,234 @@
+package main
+
+import (
+	"fmt"
+	"os"
+	"path"
+	"strings"
+
+	"github.com/consensys/gnark-crypto/ecc/bls12-377/fr"
+	"github.com/consensys/go-corset/pkg/hir"
+	sc "github.com/consensys/go-corset/pkg/schema"
+	tr "github.com/consensys/go-corset/pkg/trace"
+	"github.com/consensys/go-corset/pkg/trace/json"
+	log "github.com/sirupsen/logrus"
+	"github.com/spf13/cobra"
+)
+
+func main() {
+	err := rootCmd.Execute()
+	if err != nil {
+		os.Exit(1)
+	}
+}
+
+func init() {
+	rootCmd.Flags().BoolP("toggle", "t", false, "Help message for toggle")
+}
+
+// rootCmd represents the base command when called without any subcommands
+var rootCmd = &cobra.Command{
+	Use:   "testgen",
+	Short: "Test generation utility for go-corset.",
+	Run: func(cmd *cobra.Command, args []string) {
+		if len(args) != 1 {
+			fmt.Println(cmd.UsageString())
+			os.Exit(1)
+		}
+		model := args[0]
+		// Lookup model
+		for _, m := range models {
+			if m.Name == model {
+				// Read schema
+				filename := fmt.Sprintf("%s.lisp", m.Name)
+				schema := readSchemaFile(path.Join("testdata", filename))
+				// Generate & split traces
+				valid, invalid := generateTestTraces(m, schema)
+				// Write out
+				writeTestTraces(m, "accepts", schema, valid)
+				writeTestTraces(m, "rejects", schema, invalid)
+				os.Exit(0)
+			}
+		}
+		//
+		fmt.Printf("unknown model \"%s\"\n", model)
+		os.Exit(1)
+	},
+}
+
+// Model represents a hard-coded oracle for a given test.
+type Model struct {
+	// Name of the model in question
+	Name string
+	// Predicate for determining which trace to accept
+	Oracle func(sc.Schema, tr.Trace) bool
+}
+
+var models []Model = []Model{
+	{"memory", memoryModel},
+}
+
+// Generate test traces
+func generateTestTraces(model Model, schema sc.Schema) ([]tr.Trace, []tr.Trace) {
+	// NOTE: This is really a temporary solution for now.  It doesn't handle
+	// length multipliers.  It doesn't allow for modules with different heights.
+	// It uses a fixed pool.
+	pool := []fr.Element{fr.NewElement(0), fr.NewElement(1), fr.NewElement(2)}
+	//
+	enumerator := sc.NewTraceEnumerator(2, schema, pool)
+	valid := make([]tr.Trace, 0)
+	invalid := make([]tr.Trace, 0)
+	// Generate and split the traces
+	for enumerator.HasNext() {
+		trace := enumerator.Next()
+		// Check whether trace is valid or not (according to the oracle)
+		if model.Oracle(schema, trace) {
+			valid = append(valid, trace)
+		} else {
+			invalid = append(invalid, trace)
+		}
+	}
+	// Done
+	return valid, invalid
+}
+
+func writeTestTraces(model Model, ext string, schema sc.Schema, traces []tr.Trace) {
+	var sb strings.Builder
+	// Construct filename
+	filename := fmt.Sprintf("testdata/%s.auto.%s", model.Name, ext)
+	// Generate lines
+	for _, trace := range traces {
+		raw := traceToColumns(schema, trace)
+		json := json.ToJsonString(raw)
+		sb.WriteString(json)
+		sb.WriteString("\n")
+	}
+	// Write the file
+	if err := os.WriteFile(filename, []byte(sb.String()), 0644); err != nil {
+		panic(err)
+	}
+	// Log what happened
+	log.Infof("Wrote %s\n", filename)
+}
+
+// Convert a trace into an array of raw columns.
+func traceToColumns(schema sc.Schema, trace tr.Trace) []tr.RawColumn {
+	ncols := schema.InputColumns().Count()
+	cols := make([]tr.RawColumn, ncols)
+	i := 0
+	// Convert each column
+	for iter := schema.InputColumns(); iter.HasNext(); {
+		sc_col := iter.Next()
+		// Lookup the column data
+		tr_col := findColumn(sc_col.Context().Module(), sc_col.Name(), schema, trace)
+		// Determine module name
+		mod := schema.Modules().Nth(sc_col.Context().Module())
+		// Assignt the raw colmn
+		cols[i] = tr.RawColumn{Module: mod.Name(), Name: sc_col.Name(), Data: tr_col.Data()}
+		//
+		i++
+	}
+	//
+	return cols
+}
+
+func readSchemaFile(filename string) *hir.Schema {
+	// Read schema file
+	bytes, err := os.ReadFile(filename)
+	// Handle errors
+	if err != nil {
+		fmt.Println(err)
+		os.Exit(1)
+	}
+	// Attempt to parse schema
+	schema, err2 := hir.ParseSchemaString(string(bytes))
+	// Check whether parsed successfully or not
+	if err2 == nil {
+		// Ok
+		return schema
+	}
+	// Errors
+	fmt.Println(err2)
+	os.Exit(1)
+	// unreachable
+	return nil
+}
+
+func findColumn(mod uint, col string, schema sc.Schema, trace tr.Trace) tr.Column {
+	cid, ok := sc.ColumnIndexOf(schema, mod, col)
+	if !ok {
+		panic(fmt.Sprintf("unknown column \"%s\"", col))
+	}
+	// Done
+	return trace.Column(cid)
+}
+
+// ============================================================================
+// Models
+// ============================================================================
+
+func memoryModel(schema sc.Schema, trace tr.Trace) bool {
+	TWO_1 := fr.NewElement(2)
+	TWO_8 := fr.NewElement(256)
+	TWO_16 := fr.NewElement(65536)
+	TWO_32 := fr.NewElement(4294967296)
+	//
+	PC := findColumn(0, "PC", schema, trace).Data()
+	RW := findColumn(0, "RW", schema, trace).Data()
+	ADDR := findColumn(0, "ADDR", schema, trace).Data()
+	VAL := findColumn(0, "VAL", schema, trace).Data()
+	// Configure memory model
+	memory := make(map[fr.Element]fr.Element, 0)
+	//
+	for i := uint(0); i < PC.Len(); i++ {
+		pc_i := PC.Get(i)
+		rw_i := RW.Get(i)
+		addr_i := ADDR.Get(i)
+		val_i := VAL.Get(i)
+		// Type constraints
+		t_pc := pc_i.Cmp(&TWO_16) < 0
+		t_rw := rw_i.Cmp(&TWO_1) < 0
+		t_addr := addr_i.Cmp(&TWO_32) < 0
+		t_val := val_i.Cmp(&TWO_8) < 0
+		// Check type constraints
+		if !(t_pc && t_rw && t_addr && t_val) {
+			return false
+		}
+		// Heartbeat 1
+		h1 := i != 0 || pc_i.IsZero()
+		// Heartbeat 2
+		h2 := i == 0 || pc_i.IsZero() || isIncremented(PC.Get(i-1), pc_i)
+		// Heartbeat 3
+		h3 := i == 0 || !pc_i.IsZero() || PC.Get(i-1) == pc_i
+		// Heartbeat 4
+		h4 := !pc_i.IsZero() || (rw_i.IsZero() && addr_i.IsZero() && val_i.IsZero())
+		// Check heartbeat constraints
+		if !(h1 && h2 && h3 && h4) {
+			return false
+		}
+		// Check reading / writing
+		if rw_i.IsOne() {
+			// Write
+			memory[addr_i] = val_i
+		} else {
+			v := memory[addr_i]
+			// Check read matches
+			if v.Cmp(&val_i) != 0 {
+				return false
+			}
+		}
+	}
+	// Success
+	return true
+}
+
+// ============================================================================
+// Helpers
+// ============================================================================
+
+// Check a given element is the previous element plus one.
+func isIncremented(before fr.Element, after fr.Element) bool {
+	after.Sub(&after, &before)
+	//
+	return after.IsOne()
+}
diff --git a/pkg/air/schema.go b/pkg/air/schema.go
index fe02603c..5ad317cd 100644
--- a/pkg/air/schema.go
+++ b/pkg/air/schema.go
@@ -29,7 +29,7 @@ type PermutationConstraint = *constraint.PermutationConstraint
 // PropertyAssertion captures the notion of an arbitrary property which should
 // hold for all acceptable traces.  However, such a property is not enforced by
 // the prover.
-type PropertyAssertion = *schema.PropertyAssertion[constraint.ZeroTest[schema.Evaluable]]
+type PropertyAssertion = *schema.PropertyAssertion[schema.Testable]
 
 // Schema for AIR traces which is parameterised on a notion of computation as
 // permissible in computed columns.
@@ -134,6 +134,11 @@ func (p *Schema) AddPermutationConstraint(targets []uint, sources []uint) {
 	p.constraints = append(p.constraints, constraint.NewPermutationConstraint(targets, sources))
 }
 
+// AddPropertyAssertion appends a new property assertion.
+func (p *Schema) AddPropertyAssertion(handle string, context trace.Context, assertion schema.Testable) {
+	p.assertions = append(p.assertions, schema.NewPropertyAssertion(handle, context, assertion))
+}
+
 // AddVanishingConstraint appends a new vanishing constraint.
 func (p *Schema) AddVanishingConstraint(handle string, context trace.Context, domain *int, expr Expr) {
 	if context.Module() >= uint(len(p.modules)) {
@@ -162,6 +167,14 @@ func (p *Schema) InputColumns() util.Iterator[schema.Column] {
 		func(d schema.Declaration) util.Iterator[schema.Column] { return d.Columns() })
 }
 
+// Assertions returns an iterator over the property assertions of this
+// schema.  These are properties which should hold true for any valid trace
+// (though, of course, may not hold true for an invalid trace).
+func (p *Schema) Assertions() util.Iterator[schema.Constraint] {
+	properties := util.NewArrayIterator(p.assertions)
+	return util.NewCastIterator[PropertyAssertion, schema.Constraint](properties)
+}
+
 // Assignments returns an array over the assignments of this schema.  That
 // is, the subset of declarations whose trace values can be computed from
 // the inputs.
diff --git a/pkg/cmd/check.go b/pkg/cmd/check.go
index ef3b43e5..a749682a 100644
--- a/pkg/cmd/check.go
+++ b/pkg/cmd/check.go
@@ -48,16 +48,22 @@ var checkCmd = &cobra.Command{
 		cfg.parallelExpansion = !getFlag(cmd, "sequential")
 		cfg.batchSize = getUint(cmd, "batch")
 		cfg.ansiEscapes = getFlag(cmd, "ansi-escapes")
-		//
-		stats := util.NewPerfStats()
 		// TODO: support true ranges
 		cfg.padding.Left = cfg.padding.Right
+		if !cfg.hir && !cfg.mir && !cfg.air {
+			// If IR not specified default to running all.
+			cfg.hir, cfg.mir, cfg.air = true, true, true
+		}
+		//
+		stats := util.NewPerfStats()
 		// Parse constraints
 		hirSchema = readSchemaFile(args[1])
+		//
+		stats.Log("Reading constraints file")
 		// Parse trace file
 		columns := readTraceFile(args[0])
 		//
-		stats.Log("Reading trace files")
+		stats.Log("Reading trace file")
 		// Go!
 		if !checkTraceWithLowering(columns, hirSchema, cfg) {
 			os.Exit(1)
@@ -107,28 +113,17 @@ type checkConfig struct {
 // Check a given trace is consistently accepted (or rejected) at the different
 // IR levels.
 func checkTraceWithLowering(cols []tr.RawColumn, schema *hir.Schema, cfg checkConfig) bool {
-	hir := cfg.hir
-	mir := cfg.mir
-	air := cfg.air
-
-	if !hir && !mir && !air {
-		// If IR not specified default to running all.
-		hir = true
-		mir = true
-		air = true
-	}
-	//
 	res := true
 	// Process individually
-	if hir {
+	if cfg.hir {
 		res = checkTrace("HIR", cols, schema, cfg)
 	}
 
-	if mir {
+	if cfg.mir {
 		res = checkTrace("MIR", cols, schema.LowerToMir(), cfg) && res
 	}
 
-	if air {
+	if cfg.air {
 		res = checkTrace("AIR", cols, schema.LowerToMir().LowerToAir(), cfg) && res
 	}
 
@@ -159,11 +154,16 @@ func checkTrace(ir string, cols []tr.RawColumn, schema sc.Schema, cfg checkConfi
 		// Check trace
 		stats.Log("Validating trace")
 		stats = util.NewPerfStats()
-		//
+		// Check constraints
 		if errs := sc.Accepts(cfg.batchSize, schema, trace); len(errs) > 0 {
 			reportFailures(ir, errs, trace, cfg)
 			return false
 		}
+		// Check assertions
+		if errs := sc.Asserts(cfg.batchSize, schema, trace); len(errs) > 0 {
+			reportFailures(ir, errs, trace, cfg)
+			return false
+		}
 
 		stats.Log("Checking constraints")
 	}
@@ -238,15 +238,19 @@ func reportFailures(ir string, failures []sc.Failure, trace tr.Trace, cfg checkC
 // Print a human-readable report detailing the given failure
 func reportFailure(failure sc.Failure, trace tr.Trace, cfg checkConfig) {
 	if f, ok := failure.(*constraint.VanishingFailure); ok {
-		reportVanishingFailure(f, trace, cfg)
+		cells := f.RequiredCells(trace)
+		reportConstraintFailure("constraint", f.Handle(), cells, trace, cfg)
+	} else if f, ok := failure.(*sc.AssertionFailure); ok {
+		cells := f.RequiredCells(trace)
+		reportConstraintFailure("assertion", f.Handle(), cells, trace, cfg)
 	}
 }
 
 // Print a human-readable report detailing the given failure with a vanishing constraint.
-func reportVanishingFailure(failure *constraint.VanishingFailure, trace tr.Trace, cfg checkConfig) {
+func reportConstraintFailure(kind string, handle string, cells *util.AnySortedSet[tr.CellRef],
+	trace tr.Trace, cfg checkConfig) {
 	var start uint = math.MaxUint
 	// Determine all (input) cells involved in evaluating the given constraint
-	cells := failure.RequiredCells(trace)
 	end := uint(0)
 	// Determine row bounds
 	for _, c := range cells.ToArray() {
@@ -271,7 +275,7 @@ func reportVanishingFailure(failure *constraint.VanishingFailure, trace tr.Trace
 		return cells.Contains(cell)
 	})
 	// Print out report
-	fmt.Printf("failing constraint %s:\n", failure.Handle())
+	fmt.Printf("failing %s %s:\n", kind, handle)
 	tp.Print(trace)
 	fmt.Println()
 }
diff --git a/pkg/cmd/compute.go b/pkg/cmd/compute.go
deleted file mode 100644
index d70ee824..00000000
--- a/pkg/cmd/compute.go
+++ /dev/null
@@ -1,19 +0,0 @@
-package cmd
-
-import (
-	"github.com/spf13/cobra"
-)
-
-// computeCmd represents the compute command
-var computeCmd = &cobra.Command{
-	Use:   "compute",
-	Short: "Given a set of constraints and a trace file, fill the computed columns.",
-	Long:  `Given a set of constraints and a trace file, fill the computed columns.`,
-	Run: func(cmd *cobra.Command, args []string) {
-		panic("todo")
-	},
-}
-
-func init() {
-	rootCmd.AddCommand(computeCmd)
-}
diff --git a/pkg/cmd/test.go b/pkg/cmd/test.go
new file mode 100644
index 00000000..9fd9b4a5
--- /dev/null
+++ b/pkg/cmd/test.go
@@ -0,0 +1,150 @@
+package cmd
+
+import (
+	"fmt"
+	"math"
+	"os"
+
+	"github.com/consensys/gnark-crypto/ecc/bls12-377/fr"
+	"github.com/consensys/go-corset/pkg/hir"
+	sc "github.com/consensys/go-corset/pkg/schema"
+	tr "github.com/consensys/go-corset/pkg/trace"
+	"github.com/consensys/go-corset/pkg/util"
+
+	log "github.com/sirupsen/logrus"
+	"github.com/spf13/cobra"
+)
+
+var testCmd = &cobra.Command{
+	Use:   "test [flags] constraint_file",
+	Short: "Test a set of constraints (e.g. using randomly inputs). [EXPERIMENTAL]",
+	Long: `Check a given trace against a set of constraints.
+	Constraints can be given either as lisp or bin files.  The goal is to check for
+	 properties which don't hold on valid traces`,
+	Run: func(cmd *cobra.Command, args []string) {
+		var cfg checkConfig
+		var hirSchema *hir.Schema
+
+		if len(args) != 1 {
+			fmt.Println(cmd.UsageString())
+			os.Exit(1)
+		}
+		// Configure log level
+		if getFlag(cmd, "debug") {
+			log.SetLevel(log.DebugLevel)
+		}
+		// Setup check config
+		cfg.air = getFlag(cmd, "air")
+		cfg.mir = getFlag(cmd, "mir")
+		cfg.hir = getFlag(cmd, "hir")
+		cfg.expand = !getFlag(cmd, "raw")
+		cfg.report = getFlag(cmd, "report")
+		cfg.reportPadding = getUint(cmd, "report-context")
+		// cfg.strict = !getFlag(cmd, "warn")
+		// cfg.quiet = getFlag(cmd, "quiet")
+		cfg.padding.Right = getUint(cmd, "padding")
+		cfg.parallelExpansion = !getFlag(cmd, "sequential")
+		cfg.batchSize = getUint(cmd, "batch")
+		cfg.ansiEscapes = getFlag(cmd, "ansi-escapes")
+		// TODO: support true ranges
+		cfg.padding.Left = cfg.padding.Right
+		// Normalise IRs
+		if !cfg.hir && !cfg.mir && !cfg.air {
+			// If IR not specified default to running all.
+			cfg.hir, cfg.mir, cfg.air = true, true, true
+		}
+		//
+		stats := util.NewPerfStats()
+		// Parse constraints
+		hirSchema = readSchemaFile(args[0])
+		//
+		stats.Log("Reading constraints file")
+		//
+		if ok := runTests(2, cfg, hirSchema); !ok {
+			// Error signal
+			os.Exit(1)
+		}
+	},
+}
+
+func runTests(nrows uint, cfg checkConfig, hirSchema *hir.Schema) bool {
+	ok := true
+	// TODO: this only tests the happy path.
+	for iter := initTraceEnumerator(nrows, hirSchema); iter.HasNext(); {
+		// Read out next trace to test
+		trace := iter.Next()
+		// Test this specific trace
+		ok = testTraceWithLowering(trace, hirSchema, cfg) && ok
+	}
+	//
+	return ok
+}
+
+// Check a given trace is consistently accepted (or rejected) at the different
+// IR levels.
+func testTraceWithLowering(trace tr.Trace, schema *hir.Schema, cfg checkConfig) bool {
+	ok := true
+	// Check whether assertions hold for this trace
+	asserts := sc.Asserts(cfg.batchSize, schema, trace)
+	// Process individually
+	if cfg.hir {
+		ok = testTrace("HIR", asserts, trace, schema, cfg) && ok
+	}
+
+	if cfg.mir {
+		ok = testTrace("MIR", asserts, trace, schema.LowerToMir(), cfg) && ok
+	}
+
+	if cfg.air {
+		ok = testTrace("AIR", asserts, trace, schema.LowerToMir().LowerToAir(), cfg) && ok
+	}
+
+	return ok
+}
+
+func testTrace(ir string, asserts []sc.Failure, trace tr.Trace, schema sc.Schema, cfg checkConfig) bool {
+	ok := true
+	//
+	for n := cfg.padding.Left; n <= cfg.padding.Right; n++ {
+		// Check constraints
+		if errs := sc.Accepts(cfg.batchSize, schema, trace); len(asserts) > 0 && len(errs) == 0 {
+			// Trace accepts, but at least one assertion has failed.
+			reportFailures(ir, asserts, trace, cfg)
+			// Indicate all is not well
+			ok = false
+		}
+	}
+	// Done
+	return ok
+}
+
+// Constructs a (lazy) enumerator over the set of traces to be used for testing.
+func initTraceEnumerator(nrows uint, hirSchema *hir.Schema) util.Enumerator[tr.Trace] {
+	// NOTE: This is really a temporary solution for now.  It doesn't handle
+	// length multipliers.  It doesn't allow for modules with different heights.
+	// It uses a fixed pool.
+	pool := []fr.Element{fr.NewElement(0), fr.NewElement(1), fr.NewElement(2),
+		fr.NewElement(3), fr.NewElement(4), fr.NewElement(5)}
+	// Done
+	return sc.NewTraceEnumerator(nrows, hirSchema, pool)
+}
+
+func init() {
+	rootCmd.AddCommand(testCmd)
+	testCmd.Flags().Bool("report", false, "report details of failure for debugging")
+	testCmd.Flags().Uint("report-context", 2, "specify number of rows to show eitherside of failure in report")
+	testCmd.Flags().Bool("raw", false, "assume input trace already expanded")
+	testCmd.Flags().Bool("hir", false, "check at HIR level")
+	testCmd.Flags().Bool("mir", false, "check at MIR level")
+	testCmd.Flags().Bool("air", false, "check at AIR level")
+	// testCmd.Flags().BoolP("warn", "w", false, "report warnings instead of failing for certain errors"+
+	// 	"(e.g. unknown columns in the trace)")
+	testCmd.Flags().BoolP("debug", "d", false, "report debug logs")
+	//testCmd.Flags().BoolP("quiet", "q", false, "suppress output (e.g. warnings)")
+	testCmd.Flags().Bool("sequential", false, "perform sequential trace expansion")
+	testCmd.Flags().Uint("padding", 0, "specify amount of (front) padding to apply")
+	testCmd.Flags().UintP("batch", "b", math.MaxUint, "specify batch size for constraint checking")
+	testCmd.Flags().Int("spillage", -1,
+		"specify amount of splillage to account for (where -1 indicates this should be inferred)")
+	testCmd.Flags().Bool("ansi-escapes", true, "specify whether to allow ANSI escapes or not (e.g. for colour reports)")
+}
diff --git a/pkg/hir/schema.go b/pkg/hir/schema.go
index abba55b5..73bfcd24 100644
--- a/pkg/hir/schema.go
+++ b/pkg/hir/schema.go
@@ -153,6 +153,14 @@ func (p *Schema) InputColumns() util.Iterator[sc.Column] {
 		func(d schema.Declaration) util.Iterator[schema.Column] { return d.Columns() })
 }
 
+// Assertions returns an iterator over the property assertions of this
+// schema.  These are properties which should hold true for any valid trace
+// (though, of course, may not hold true for an invalid trace).
+func (p *Schema) Assertions() util.Iterator[schema.Constraint] {
+	properties := util.NewArrayIterator(p.assertions)
+	return util.NewCastIterator[PropertyAssertion, schema.Constraint](properties)
+}
+
 // Assignments returns an array over the assignments of this sc.  That
 // is, the subset of declarations whose trace values can be computed from
 // the inputs.
diff --git a/pkg/mir/lower.go b/pkg/mir/lower.go
index 07a6a87b..b5b1e811 100644
--- a/pkg/mir/lower.go
+++ b/pkg/mir/lower.go
@@ -39,6 +39,10 @@ func (p *Schema) LowerToAir() *air.Schema {
 	for _, c := range p.constraints {
 		lowerConstraintToAir(c, airSchema)
 	}
+	// Add assertions (these do not need to be lowered)
+	for _, assertion := range p.assertions {
+		airSchema.AddPropertyAssertion(assertion.Handle(), assertion.Context(), assertion.Property())
+	}
 	// Done
 	return airSchema
 }
diff --git a/pkg/mir/schema.go b/pkg/mir/schema.go
index ef49766b..1116bebe 100644
--- a/pkg/mir/schema.go
+++ b/pkg/mir/schema.go
@@ -149,6 +149,14 @@ func (p *Schema) InputColumns() util.Iterator[schema.Column] {
 		func(d schema.Declaration) util.Iterator[schema.Column] { return d.Columns() })
 }
 
+// Assertions returns an iterator over the property assertions of this
+// schema.  These are properties which should hold true for any valid trace
+// (though, of course, may not hold true for an invalid trace).
+func (p *Schema) Assertions() util.Iterator[schema.Constraint] {
+	properties := util.NewArrayIterator(p.assertions)
+	return util.NewCastIterator[PropertyAssertion, schema.Constraint](properties)
+}
+
 // Assignments returns an array over the assignments of this schema.  That
 // is, the subset of declarations whose trace values can be computed from
 // the inputs.
diff --git a/pkg/schema/assertion.go b/pkg/schema/assertion.go
index 47e7e0bd..52d12e0e 100644
--- a/pkg/schema/assertion.go
+++ b/pkg/schema/assertion.go
@@ -1,13 +1,54 @@
 package schema
 
 import (
-	"errors"
 	"fmt"
 
-	"github.com/consensys/go-corset/pkg/trace"
+	"github.com/consensys/go-corset/pkg/sexp"
 	tr "github.com/consensys/go-corset/pkg/trace"
+	"github.com/consensys/go-corset/pkg/util"
 )
 
+// AssertionFailure provides structural information about a failing vanishing constraint.
+type AssertionFailure struct {
+	// Handle of the failing constraint
+	handle string
+	// Constraint expression
+	constraint Testable
+	// Row on which the constraint failed
+	row uint
+}
+
+// Handle returns the handle of this constraint
+func (p *AssertionFailure) Handle() string {
+	// Construct useful error message
+	return p.handle
+}
+
+// Message provides a suitable error message
+func (p *AssertionFailure) Message() string {
+	// Construct useful error message
+	return fmt.Sprintf("assertion \"%s\" does not hold (row %d)", p.handle, p.row)
+}
+
+// Constraint returns the constraint expression itself.
+func (p *AssertionFailure) Constraint() Testable {
+	return p.constraint
+}
+
+// Row identifies the row on which this constraint failed.
+func (p *AssertionFailure) Row() uint {
+	return p.row
+}
+
+// RequiredCells identifies the cells required to evaluate the failing constraint at the failing row.
+func (p *AssertionFailure) RequiredCells(trace tr.Trace) *util.AnySortedSet[tr.CellRef] {
+	return p.constraint.RequiredCells(int(p.row), trace)
+}
+
+func (p *AssertionFailure) String() string {
+	return p.Message()
+}
+
 // PropertyAssertion is similar to a vanishing constraint but is used only for
 // debugging / testing / verification.  Unlike vanishing constraints, property
 // assertions do not represent something that the prover can enforce.  Rather,
@@ -21,7 +62,7 @@ type PropertyAssertion[T Testable] struct {
 	handle string
 	// Enclosing module for this assertion.  This restricts the asserted
 	// property to access only columns from within this module.
-	context trace.Context
+	context tr.Context
 	// The actual assertion itself, namely an expression which
 	// should hold (i.e. vanish) for every row of a trace.
 	// Observe that this can be any function which is computable
@@ -31,7 +72,7 @@ type PropertyAssertion[T Testable] struct {
 }
 
 // NewPropertyAssertion constructs a new property assertion!
-func NewPropertyAssertion[T Testable](handle string, ctx trace.Context, property T) *PropertyAssertion[T] {
+func NewPropertyAssertion[T Testable](handle string, ctx tr.Context, property T) *PropertyAssertion[T] {
 	return &PropertyAssertion[T]{handle, ctx, property}
 }
 
@@ -45,7 +86,7 @@ func (p *PropertyAssertion[T]) Handle() string {
 // Context returns the handle associated with this constraint.
 //
 //nolint:revive
-func (p *PropertyAssertion[T]) Context() trace.Context {
+func (p *PropertyAssertion[T]) Context() tr.Context {
 	return p.context
 }
 
@@ -60,19 +101,29 @@ func (p *PropertyAssertion[T]) Property() T {
 // of a table. If so, return nil otherwise return an error.
 //
 //nolint:revive
-func (p *PropertyAssertion[T]) Accepts(tr tr.Trace) error {
+func (p *PropertyAssertion[T]) Accepts(tr tr.Trace) Failure {
 	// Determine height of enclosing module
 	height := tr.Height(p.context)
 	// Iterate every row in the module
 	for k := uint(0); k < height; k++ {
 		// Check whether property holds (or was undefined)
 		if !p.property.TestAt(int(k), tr) {
-			// Construct useful error message
-			msg := fmt.Sprintf("property assertion %s does not hold (row %d)", p.handle, k)
 			// Evaluation failure
-			return errors.New(msg)
+			return &AssertionFailure{p.handle, p.property, k}
 		}
 	}
 	// All good
 	return nil
 }
+
+// Lisp converts this constraint into an S-Expression.
+//
+//nolint:revive
+func (p *PropertyAssertion[T]) Lisp(schema Schema) sexp.SExp {
+	// Construct the list
+	return sexp.NewList([]sexp.SExp{
+		sexp.NewSymbol("assert"),
+		sexp.NewSymbol(p.handle),
+		p.property.Lisp(schema),
+	})
+}
diff --git a/pkg/schema/enumerator.go b/pkg/schema/enumerator.go
new file mode 100644
index 00000000..0c8154b0
--- /dev/null
+++ b/pkg/schema/enumerator.go
@@ -0,0 +1,77 @@
+package schema
+
+import (
+	"github.com/consensys/gnark-crypto/ecc/bls12-377/fr"
+	tr "github.com/consensys/go-corset/pkg/trace"
+	"github.com/consensys/go-corset/pkg/util"
+	log "github.com/sirupsen/logrus"
+)
+
+// ============================================================================
+// TraceEnumerator
+// ============================================================================
+
+// TraceEnumerator is an adaptor which surrounds an enumerator and, essentially,
+// converts flat sequences of elements into traces.
+type TraceEnumerator struct {
+	// Schema for which traces are being generated
+	schema Schema
+	// Number of lines
+	lines uint
+	// Enumerate sequences of elements
+	enumerator util.Enumerator[[]fr.Element]
+}
+
+// NewTraceEnumerator constructs an enumerator for all traces matching the
+// given column specifications using elements sourced from the given pool.
+func NewTraceEnumerator(lines uint, schema Schema, pool []fr.Element) util.Enumerator[tr.Trace] {
+	ncells := schema.InputColumns().Count() * lines
+	// Construct the enumerator
+	enumerator := util.EnumerateElements[fr.Element](ncells, pool)
+	// Done
+	return &TraceEnumerator{schema, lines, enumerator}
+}
+
+// Next returns the next trace in the enumeration
+func (p *TraceEnumerator) Next() tr.Trace {
+	ncols := p.schema.InputColumns().Count()
+	elems := p.enumerator.Next()
+	cols := make([]tr.RawColumn, ncols)
+	//
+	i, j := 0, 0
+	// Construct each column from the sequence
+	for iter := p.schema.InputColumns(); iter.HasNext(); {
+		col := iter.Next()
+		data := util.NewFrArray(p.lines, 256)
+		// Slice nrows values from elems
+		for k := uint(0); k < p.lines; k++ {
+			data.Set(k, elems[j])
+			// Consume element from generated sequence
+			j++
+		}
+		// Construct raw column
+		modName := p.schema.Modules().Nth(col.context.Module()).name
+		cols[i] = tr.RawColumn{Module: modName, Name: col.Name(), Data: data}
+		i++
+	}
+	// Finally, build the trace.
+	builder := NewTraceBuilder(p.schema).Expand(true).Parallel(false).Padding(0)
+	// Build the trace
+	trace, errs := builder.Build(cols)
+	// Handle errors
+	if errs != nil {
+		// Should be unreachable, since control the trace!
+		for _, err := range errs {
+			log.Error(err)
+		}
+		// Fail
+		panic("invalid trace constructed")
+	}
+	// Done
+	return trace
+}
+
+// HasNext checks whether the enumeration has more elements (or not).
+func (p *TraceEnumerator) HasNext() bool {
+	return p.enumerator.HasNext()
+}
diff --git a/pkg/schema/schema.go b/pkg/schema/schema.go
index e072c2d1..c5af034d 100644
--- a/pkg/schema/schema.go
+++ b/pkg/schema/schema.go
@@ -12,6 +12,11 @@ import (
 
 // Schema represents a schema which can be used to manipulate a trace.
 type Schema interface {
+	// Assertions returns an iterator over the property assertions of this
+	// schema.  These are properties which should hold true for any valid trace
+	// (though, of course, may not hold true for an invalid trace).
+	Assertions() util.Iterator[Constraint]
+
 	// Assignments returns an iterator over the assignments of this schema.  That
 	// is, the subset of declarations whose trace values can be computed from
 	// the inputs.
diff --git a/pkg/schema/schemas.go b/pkg/schema/schemas.go
index c33331c1..b9657e52 100644
--- a/pkg/schema/schemas.go
+++ b/pkg/schema/schemas.go
@@ -68,20 +68,35 @@ func ContextOfColumns(cols []uint, schema Schema) tr.Context {
 	return ctx
 }
 
-// Accepts determines whether this schema will accept a given trace.  That
-// is, whether or not the given trace adheres to the schema.  A trace can fail
-// to adhere to the schema for a variety of reasons, such as having a constraint
-// which does not hold.
-//
-//nolint:revive
+// Accepts determines whether this schema will accept a given trace.  That is,
+// whether or not the given trace adheres to the schema constraints.  A trace
+// can fail to adhere to the schema for a variety of reasons, such as having a
+// constraint which does not hold.  Observe that this does not check assertions
+// within the schema hold.
 func Accepts(batchsize uint, schema Schema, trace tr.Trace) []Failure {
 	errors := make([]Failure, 0)
-	iter := schema.Constraints()
 	// Initialise batch number (for debugging purposes)
 	batch := uint(0)
 	// Process constraints in batches
-	for iter.HasNext() {
-		errs := processConstraintBatch(batch, batchsize, iter, trace)
+	for iter := schema.Constraints(); iter.HasNext(); {
+		errs := processConstraintBatch("Constraint", batch, batchsize, iter, trace)
+		errors = append(errors, errs...)
+		// Increment batch number
+		batch++
+	}
+	// Success
+	return errors
+}
+
+// Asserts determines whether or not this schema will "assert" a given trace.
+// That is, whether or not the given trace adheres to the schema assertions.
+func Asserts(batchsize uint, schema Schema, trace tr.Trace) []Failure {
+	errors := make([]Failure, 0)
+	// Initialise batch number (for debugging purposes)
+	batch := uint(0)
+	// Process assertions in batches
+	for iter := schema.Assertions(); iter.HasNext(); {
+		errs := processConstraintBatch("Assertion", batch, batchsize, iter, trace)
 		errors = append(errors, errs...)
 		// Increment batch number
 		batch++
@@ -91,7 +106,8 @@ func Accepts(batchsize uint, schema Schema, trace tr.Trace) []Failure {
 }
 
 // Process a given set of constraints in a single batch whilst recording all constraint failures.
-func processConstraintBatch(batch uint, batchsize uint, iter util.Iterator[Constraint], trace tr.Trace) []Failure {
+func processConstraintBatch(logtitle string, batch uint, batchsize uint, iter util.Iterator[Constraint],
+	trace tr.Trace) []Failure {
 	n := uint(0)
 	c := make(chan Failure, 1024)
 	errors := make([]Failure, 0)
@@ -114,7 +130,7 @@ func processConstraintBatch(batch uint, batchsize uint, iter util.Iterator[Const
 		}
 	}
 	// Log stats about this batch
-	stats.Log(fmt.Sprintf("Constraint batch %d", batch))
+	stats.Log(fmt.Sprintf("%s batch %d", logtitle, batch))
 	//
 	return errors
 }
diff --git a/pkg/test/arrays_test.go b/pkg/test/arrays_test.go
new file mode 100644
index 00000000..4acc23cd
--- /dev/null
+++ b/pkg/test/arrays_test.go
@@ -0,0 +1,54 @@
+package test
+
+import (
+	"reflect"
+	"testing"
+
+	"github.com/consensys/go-corset/pkg/util"
+)
+
+func Test_RemoveMatching_01(t *testing.T) {
+	check_RemoveMatching(t, []int{1, 2}, 1, []int{2})
+}
+
+func Test_RemoveMatching_02(t *testing.T) {
+	check_RemoveMatching(t, []int{1, 2}, 2, []int{1})
+}
+
+func Test_RemoveMatching_03(t *testing.T) {
+	check_RemoveMatching(t, []int{1, 2, 3}, 1, []int{2, 3})
+}
+
+func Test_RemoveMatching_04(t *testing.T) {
+	check_RemoveMatching(t, []int{2, 1, 3}, 1, []int{2, 3})
+}
+
+func Test_RemoveMatching_05(t *testing.T) {
+	check_RemoveMatching(t, []int{2, 3, 1}, 1, []int{2, 3})
+}
+
+func Test_RemoveMatching_06(t *testing.T) {
+	check_RemoveMatching(t, []int{1, 2, 3, 1}, 1, []int{2, 3})
+}
+
+func Test_RemoveMatching_07(t *testing.T) {
+	check_RemoveMatching(t, []int{2, 1, 3, 1}, 1, []int{2, 3})
+}
+func Test_RemoveMatching_08(t *testing.T) {
+	check_RemoveMatching(t, []int{2, 3, 1, 1}, 1, []int{2, 3})
+}
+
+func Test_RemoveMatching_09(t *testing.T) {
+	check_RemoveMatching(t, []int{1, 2, 1, 3}, 1, []int{2, 3})
+}
+
+func Test_RemoveMatching_10(t *testing.T) {
+	check_RemoveMatching(t, []int{1, 1, 2, 3}, 1, []int{2, 3})
+}
+
+func check_RemoveMatching(t *testing.T, original []int, item int, expected []int) {
+	actual := util.RemoveMatching(original, func(ith int) bool { return ith == item })
+	if !reflect.DeepEqual(actual, expected) {
+		t.Errorf("removing %d from %v got %v", item, original, actual)
+	}
+}
diff --git a/pkg/test/enumerator_test.go b/pkg/test/enumerator_test.go
new file mode 100644
index 00000000..b56f458c
--- /dev/null
+++ b/pkg/test/enumerator_test.go
@@ -0,0 +1,79 @@
+package test
+
+import (
+	"testing"
+
+	"github.com/consensys/go-corset/pkg/util"
+)
+
+func Test_Enumerator_1_1(t *testing.T) {
+	enumerator := util.EnumerateElements[uint](1, []uint{0})
+	checkEnumerator(t, enumerator, [][]uint{{0}}, arrayEquals)
+}
+
+func Test_Enumerator_1_2(t *testing.T) {
+	enumerator := util.EnumerateElements[uint](1, []uint{0, 1})
+	checkEnumerator(t, enumerator, [][]uint{{0}, {1}}, arrayEquals)
+}
+
+func Test_Enumerator_1_3(t *testing.T) {
+	enumerator := util.EnumerateElements[uint](1, []uint{0, 1, 2})
+	checkEnumerator(t, enumerator, [][]uint{{0}, {1}, {2}}, arrayEquals)
+}
+
+func Test_Enumerator_2_1(t *testing.T) {
+	enumerator := util.EnumerateElements[uint](2, []uint{0})
+	checkEnumerator(t, enumerator, [][]uint{{0, 0}}, arrayEquals)
+}
+
+func Test_Enumerator_2_2(t *testing.T) {
+	enumerator := util.EnumerateElements[uint](2, []uint{0, 1})
+	checkEnumerator(t, enumerator, [][]uint{{0, 0}, {1, 0}, {0, 1}, {1, 1}}, arrayEquals)
+}
+
+func Test_Enumerator_2_3(t *testing.T) {
+	enumerator := util.EnumerateElements[uint](2, []uint{0, 1, 2})
+	checkEnumerator(t, enumerator, [][]uint{
+		{0, 0}, {1, 0}, {2, 0}, {0, 1}, {1, 1}, {2, 1}, {0, 2}, {1, 2}, {2, 2}}, arrayEquals)
+}
+
+func Test_Enumerator_3_1(t *testing.T) {
+	enumerator := util.EnumerateElements[uint](3, []uint{0})
+	checkEnumerator(t, enumerator, [][]uint{{0, 0, 0}}, arrayEquals)
+}
+func Test_Enumerator_3_2(t *testing.T) {
+	enumerator := util.EnumerateElements[uint](3, []uint{0, 1})
+	checkEnumerator(t, enumerator, [][]uint{
+		{0, 0, 0}, {1, 0, 0}, {0, 1, 0}, {1, 1, 0}, {0, 0, 1}, {1, 0, 1}, {0, 1, 1}, {1, 1, 1}}, arrayEquals)
+}
+
+// ===================================================================
+// Test Helpers
+// ===================================================================
+
+func checkEnumerator[E any](t *testing.T, enumerator util.Enumerator[E], expected []E, eq func(E, E) bool) {
+	for i := 0; i < len(expected); i++ {
+		ith := enumerator.Next()
+		if !eq(ith, expected[i]) {
+			t.Errorf("expected %s, got %s", any(expected[i]), any(ith))
+		}
+	}
+	// Sanity check lengths match
+	if enumerator.HasNext() {
+		t.Errorf("expected %d elements, got more", len(expected))
+	}
+}
+
+func arrayEquals[T comparable](lhs []T, rhs []T) bool {
+	if len(lhs) != len(rhs) {
+		return false
+	}
+	// Check each item in turn
+	for i := 0; i < len(lhs); i++ {
+		if lhs[i] != rhs[i] {
+			return false
+		}
+	}
+	// Done
+	return true
+}
diff --git a/pkg/test/hashset_test.go b/pkg/test/hashset_test.go
index 24f224e4..b06f2ea2 100644
--- a/pkg/test/hashset_test.go
+++ b/pkg/test/hashset_test.go
@@ -14,32 +14,32 @@ func Test_HashSet_01(t *testing.T) {
 }
 
 func Test_HashSet_02(t *testing.T) {
-	items := util.GenerateRandomInputs(10, 32)
+	items := util.GenerateRandomUints(10, 32)
 	check_HashSet(t, items)
 }
 
 func Test_HashSet_03(t *testing.T) {
-	items := util.GenerateRandomInputs(100, 32)
+	items := util.GenerateRandomUints(100, 32)
 	check_HashSet(t, items)
 }
 
 func Test_HashSet_04(t *testing.T) {
-	items := util.GenerateRandomInputs(1000, 32)
+	items := util.GenerateRandomUints(1000, 32)
 	check_HashSet(t, items)
 }
 
 func Test_HashSet_05(t *testing.T) {
-	items := util.GenerateRandomInputs(100000, 32)
+	items := util.GenerateRandomUints(100000, 32)
 	check_HashSet(t, items)
 }
 
 func TestSlow_HashSet_08(t *testing.T) {
-	items := util.GenerateRandomInputs(100000, 64)
+	items := util.GenerateRandomUints(100000, 64)
 	check_HashSet(t, items)
 }
 
 func TestSlow_HashSet_09(t *testing.T) {
-	items := util.GenerateRandomInputs(100000, 128)
+	items := util.GenerateRandomUints(100000, 128)
 	check_HashSet(t, items)
 }
 
diff --git a/pkg/test/ir_test.go b/pkg/test/ir_test.go
index 393e2373..082646ce 100644
--- a/pkg/test/ir_test.go
+++ b/pkg/test/ir_test.go
@@ -497,14 +497,27 @@ func Check(t *testing.T, test string) {
 		t.Fatalf("Error parsing %s.lisp: %s\n", test, err)
 	}
 	// Check valid traces are accepted
-	accepts := ReadTracesFile(test, "accepts")
-	CheckTraces(t, test, true, true, accepts, schema)
+	accepts_file := fmt.Sprintf("%s.%s", test, "accepts")
+	accepts := ReadTracesFile(accepts_file)
+	CheckTraces(t, accepts_file, true, true, accepts, schema)
 	// Check invalid traces are rejected
-	rejects := ReadTracesFile(test, "rejects")
-	CheckTraces(t, test, false, true, rejects, schema)
+	rejects_file := fmt.Sprintf("%s.%s", test, "rejects")
+	rejects := ReadTracesFile(rejects_file)
+	CheckTraces(t, rejects_file, false, true, rejects, schema)
 	// Check expanded traces are rejected
-	expands := ReadTracesFile(test, "expanded")
-	CheckTraces(t, test, false, false, expands, schema)
+	expands_file := fmt.Sprintf("%s.%s", test, "expanded")
+	expands := ReadTracesFile(expands_file)
+	CheckTraces(t, expands_file, false, false, expands, schema)
+	// Check auto-generated valid traces (if applicable)
+	auto_accepts_file := fmt.Sprintf("%s.%s", test, "auto.accepts")
+	if auto_accepts := ReadTracesFileIfExists(auto_accepts_file); auto_accepts != nil {
+		CheckTraces(t, auto_accepts_file, true, true, auto_accepts, schema)
+	}
+	// Check auto-generated invalid traces (if applicable)
+	auto_rejects_file := fmt.Sprintf("%s.%s", test, "auto.rejects")
+	if auto_rejects := ReadTracesFileIfExists(auto_rejects_file); auto_rejects != nil {
+		CheckTraces(t, auto_rejects_file, false, true, auto_rejects, schema)
+	}
 }
 
 // Check a given set of tests have an expected outcome (i.e. are
@@ -553,11 +566,11 @@ func checkTrace(t *testing.T, inputs []trace.RawColumn, expand bool, id traceId,
 		// Process what happened versus what was supposed to happen.
 		if !accepted && id.expected {
 			//table.PrintTrace(tr)
-			t.Errorf("Trace rejected incorrectly (%s, %s.accepts, line %d with padding %d): %s",
+			t.Errorf("Trace rejected incorrectly (%s, %s, line %d with padding %d): %s",
 				id.ir, id.test, id.line, id.padding, errs)
 		} else if accepted && !id.expected {
 			//printTrace(tr)
-			t.Errorf("Trace accepted incorrectly (%s, %s.rejects, line %d with padding %d)",
+			t.Errorf("Trace accepted incorrectly (%s, %s, line %d with padding %d)",
 				id.ir, id.test, id.line, id.padding)
 		}
 	}
@@ -584,8 +597,8 @@ type traceId struct {
 
 // ReadTracesFile reads a file containing zero or more traces expressed as JSON, where
 // each trace is on a separate line.
-func ReadTracesFile(name string, ext string) [][]trace.RawColumn {
-	lines := ReadInputFile(name, ext)
+func ReadTracesFile(filename string) [][]trace.RawColumn {
+	lines := ReadInputFile(filename)
 	traces := make([][]trace.RawColumn, len(lines))
 	// Read constraints line by line
 	for i, line := range lines {
@@ -593,7 +606,7 @@ func ReadTracesFile(name string, ext string) [][]trace.RawColumn {
 		if line != "" && !strings.HasPrefix(line, ";;") {
 			tr, err := json.FromBytes([]byte(line))
 			if err != nil {
-				msg := fmt.Sprintf("%s.%s:%d: %s", name, ext, i+1, err)
+				msg := fmt.Sprintf("%s:%d: %s", filename, i+1, err)
 				panic(msg)
 			}
 
@@ -604,10 +617,20 @@ func ReadTracesFile(name string, ext string) [][]trace.RawColumn {
 	return traces
 }
 
+func ReadTracesFileIfExists(name string) [][]trace.RawColumn {
+	filename := fmt.Sprintf("%s/%s", TestDir, name)
+	// Check whether it exists or not
+	if _, err := os.Stat(filename); err != nil {
+		return nil
+	}
+	// Yes it does
+	return ReadTracesFile(name)
+}
+
 // ReadInputFile reads an input file as a sequence of lines.
-func ReadInputFile(name string, ext string) []string {
-	name = fmt.Sprintf("%s/%s.%s", TestDir, name, ext)
-	file, err := os.Open(name)
+func ReadInputFile(filename string) []string {
+	filename = fmt.Sprintf("%s/%s", TestDir, filename)
+	file, err := os.Open(filename)
 	// Check whether file exists
 	if errors.Is(err, os.ErrNotExist) {
 		return []string{}
diff --git a/pkg/test/sortedset_test.go b/pkg/test/sortedset_test.go
index ac46bcb3..8632b21e 100644
--- a/pkg/test/sortedset_test.go
+++ b/pkg/test/sortedset_test.go
@@ -59,7 +59,7 @@ func array_contains(items []uint, element uint) bool {
 }
 
 func check_SortedSet_Insert(t *testing.T, n uint, m uint) {
-	items := util.GenerateRandomInputs(n, m)
+	items := util.GenerateRandomUints(n, m)
 	set := toSortedSet(items)
 	anyset := toAnySortedSet(items)
 
@@ -83,8 +83,8 @@ func check_SortedSet_Insert(t *testing.T, n uint, m uint) {
 }
 
 func check_SortedSet_InsertSorted(t *testing.T, n uint, m uint) {
-	left := util.GenerateRandomInputs(n, m)
-	right := util.GenerateRandomInputs(n, m)
+	left := util.GenerateRandomUints(n, m)
+	right := util.GenerateRandomUints(n, m)
 	set := toSortedSet(left)
 	anyset := toAnySortedSet(left)
 
diff --git a/pkg/util/enumerator.go b/pkg/util/enumerator.go
new file mode 100644
index 00000000..f2bfceec
--- /dev/null
+++ b/pkg/util/enumerator.go
@@ -0,0 +1,65 @@
+package util
+
+// Enumerator abstracts the process of iterating over a sequence of elements.
+type Enumerator[T any] interface {
+	// Check whether or not there are any items remaining to visit.
+	HasNext() bool
+
+	// Get the next item, and advanced the iterator.
+	Next() T
+}
+
+// EnumerateElements returns an iterator which enumerates all arrays of size n
+// over the given set of elements.  For example, if n==2 and elems contained two
+// elements A and B, then this will return [[A,A],[A,B][B,A],[B,B]].
+func EnumerateElements[E any](n uint, elems []E) Enumerator[[]E] {
+	counters := make([]uint, n)
+	return &enumerator[E]{counters, elems}
+}
+
+type enumerator[E any] struct {
+	counters []uint
+	elements []E
+}
+
+// HasNext checks whether or not there are any items remaining to visit.
+//
+//nolint:revive
+func (p *enumerator[E]) HasNext() bool {
+	return p.counters != nil
+}
+
+// Next returns the next item, and advance the iterator.
+//
+//nolint:revive
+func (p *enumerator[E]) Next() []E {
+	rs := make([]E, len(p.counters))
+	// Copy over elements
+	for i := 0; i < len(rs); i++ {
+		rs[i] = p.elements[p.counters[i]]
+	}
+	//
+	carry := false
+	// Increment counters
+	for i := 0; i < len(p.counters); i++ {
+		ithp1 := p.counters[i] + 1
+		// Check for oveflow
+		if ithp1 != uint(len(p.elements)) {
+			// No overflow
+			p.counters[i] = ithp1
+			carry = false
+			// Done incrementing
+			break
+		}
+		// overflow
+		p.counters[i] = 0
+		carry = true
+	}
+	// Check whether finished
+	if carry {
+		// Yes, signal end of enumeration
+		p.counters = nil
+	}
+	//
+	return rs
+}
diff --git a/pkg/util/iterator.go b/pkg/util/iterator.go
index 31f4e0c6..45ccab51 100644
--- a/pkg/util/iterator.go
+++ b/pkg/util/iterator.go
@@ -6,7 +6,7 @@ type Predicate[T any] func(T) bool
 // Iterator is an adapter which sits on top of a BaseIterator and provides
 // various useful and reusable functions.
 type Iterator[T any] interface {
-	BaseIterator[T]
+	Enumerator[T]
 
 	// Append another iterator onto the end of this iterator.  Thus, when all
 	// items are visited in this iterator, iteration continues into the other.
@@ -490,16 +490,7 @@ func (p *unitIterator[T]) Nth(n uint) T {
 // Base Iterator
 // ===============================================================
 
-// BaseIterator abstracts the process of iterating over a sequence of elements.
-type BaseIterator[T any] interface {
-	// Check whether or not there are any items remaining to visit.
-	HasNext() bool
-
-	// Get the next item, and advanced the iterator.
-	Next() T
-}
-
-func baseFind[T any, S BaseIterator[T]](iter S, predicate Predicate[T]) (uint, bool) {
+func baseFind[T any, S Enumerator[T]](iter S, predicate Predicate[T]) (uint, bool) {
 	index := uint(0)
 
 	for i := iter; i.HasNext(); {
@@ -513,7 +504,7 @@ func baseFind[T any, S BaseIterator[T]](iter S, predicate Predicate[T]) (uint, b
 	return 0, false
 }
 
-func baseNth[T any, S BaseIterator[T]](iter S, n uint) T {
+func baseNth[T any, S Enumerator[T]](iter S, n uint) T {
 	index := uint(0)
 
 	for i := iter; i.HasNext(); {
diff --git a/pkg/util/random.go b/pkg/util/random.go
index fa5f8f69..d1a3e041 100644
--- a/pkg/util/random.go
+++ b/pkg/util/random.go
@@ -2,8 +2,8 @@ package util
 
 import "math/rand/v2"
 
-// GenerateRandomInputs generates n random inputs in the range 0..m.
-func GenerateRandomInputs(n, m uint) []uint {
+// GenerateRandomUints generates n random unsigned integers in the range 0..m.
+func GenerateRandomUints(n, m uint) []uint {
 	items := make([]uint, n)
 
 	for i := uint(0); i < n; i++ {
@@ -12,3 +12,16 @@ func GenerateRandomInputs(n, m uint) []uint {
 
 	return items
 }
+
+// GenerateRandomElements generates n elements selected at random from the given array.
+func GenerateRandomElements[E any](n uint, elems []E) []E {
+	items := make([]E, n)
+	m := uint(len(elems))
+
+	for i := uint(0); i < n; i++ {
+		index := rand.UintN(m)
+		items[i] = elems[index]
+	}
+
+	return items
+}
diff --git a/testdata/memory.auto.accepts b/testdata/memory.auto.accepts
new file mode 100644
index 00000000..003f7011
--- /dev/null
+++ b/testdata/memory.auto.accepts
@@ -0,0 +1,157 @@
+{"PC": [0, 0, 0], "RW": [0, 0, 0], "ADDR": [0, 0, 0], "VAL": [0, 0, 0]}
+{"PC": [0, 0, 1], "RW": [0, 0, 0], "ADDR": [0, 0, 0], "VAL": [0, 0, 0]}
+{"PC": [0, 1, 2], "RW": [0, 0, 0], "ADDR": [0, 0, 0], "VAL": [0, 0, 0]}
+{"PC": [0, 1, 2], "RW": [0, 1, 0], "ADDR": [0, 0, 0], "VAL": [0, 0, 0]}
+{"PC": [0, 0, 1], "RW": [0, 0, 1], "ADDR": [0, 0, 0], "VAL": [0, 0, 0]}
+{"PC": [0, 1, 2], "RW": [0, 0, 1], "ADDR": [0, 0, 0], "VAL": [0, 0, 0]}
+{"PC": [0, 1, 2], "RW": [0, 1, 1], "ADDR": [0, 0, 0], "VAL": [0, 0, 0]}
+{"PC": [0, 1, 2], "RW": [0, 0, 0], "ADDR": [0, 1, 0], "VAL": [0, 0, 0]}
+{"PC": [0, 1, 2], "RW": [0, 1, 0], "ADDR": [0, 1, 0], "VAL": [0, 0, 0]}
+{"PC": [0, 1, 2], "RW": [0, 0, 1], "ADDR": [0, 1, 0], "VAL": [0, 0, 0]}
+{"PC": [0, 1, 2], "RW": [0, 1, 1], "ADDR": [0, 1, 0], "VAL": [0, 0, 0]}
+{"PC": [0, 1, 2], "RW": [0, 0, 0], "ADDR": [0, 2, 0], "VAL": [0, 0, 0]}
+{"PC": [0, 1, 2], "RW": [0, 1, 0], "ADDR": [0, 2, 0], "VAL": [0, 0, 0]}
+{"PC": [0, 1, 2], "RW": [0, 0, 1], "ADDR": [0, 2, 0], "VAL": [0, 0, 0]}
+{"PC": [0, 1, 2], "RW": [0, 1, 1], "ADDR": [0, 2, 0], "VAL": [0, 0, 0]}
+{"PC": [0, 0, 1], "RW": [0, 0, 0], "ADDR": [0, 0, 1], "VAL": [0, 0, 0]}
+{"PC": [0, 1, 2], "RW": [0, 0, 0], "ADDR": [0, 0, 1], "VAL": [0, 0, 0]}
+{"PC": [0, 1, 2], "RW": [0, 1, 0], "ADDR": [0, 0, 1], "VAL": [0, 0, 0]}
+{"PC": [0, 0, 1], "RW": [0, 0, 1], "ADDR": [0, 0, 1], "VAL": [0, 0, 0]}
+{"PC": [0, 1, 2], "RW": [0, 0, 1], "ADDR": [0, 0, 1], "VAL": [0, 0, 0]}
+{"PC": [0, 1, 2], "RW": [0, 1, 1], "ADDR": [0, 0, 1], "VAL": [0, 0, 0]}
+{"PC": [0, 1, 2], "RW": [0, 0, 0], "ADDR": [0, 1, 1], "VAL": [0, 0, 0]}
+{"PC": [0, 1, 2], "RW": [0, 1, 0], "ADDR": [0, 1, 1], "VAL": [0, 0, 0]}
+{"PC": [0, 1, 2], "RW": [0, 0, 1], "ADDR": [0, 1, 1], "VAL": [0, 0, 0]}
+{"PC": [0, 1, 2], "RW": [0, 1, 1], "ADDR": [0, 1, 1], "VAL": [0, 0, 0]}
+{"PC": [0, 1, 2], "RW": [0, 0, 0], "ADDR": [0, 2, 1], "VAL": [0, 0, 0]}
+{"PC": [0, 1, 2], "RW": [0, 1, 0], "ADDR": [0, 2, 1], "VAL": [0, 0, 0]}
+{"PC": [0, 1, 2], "RW": [0, 0, 1], "ADDR": [0, 2, 1], "VAL": [0, 0, 0]}
+{"PC": [0, 1, 2], "RW": [0, 1, 1], "ADDR": [0, 2, 1], "VAL": [0, 0, 0]}
+{"PC": [0, 0, 1], "RW": [0, 0, 0], "ADDR": [0, 0, 2], "VAL": [0, 0, 0]}
+{"PC": [0, 1, 2], "RW": [0, 0, 0], "ADDR": [0, 0, 2], "VAL": [0, 0, 0]}
+{"PC": [0, 1, 2], "RW": [0, 1, 0], "ADDR": [0, 0, 2], "VAL": [0, 0, 0]}
+{"PC": [0, 0, 1], "RW": [0, 0, 1], "ADDR": [0, 0, 2], "VAL": [0, 0, 0]}
+{"PC": [0, 1, 2], "RW": [0, 0, 1], "ADDR": [0, 0, 2], "VAL": [0, 0, 0]}
+{"PC": [0, 1, 2], "RW": [0, 1, 1], "ADDR": [0, 0, 2], "VAL": [0, 0, 0]}
+{"PC": [0, 1, 2], "RW": [0, 0, 0], "ADDR": [0, 1, 2], "VAL": [0, 0, 0]}
+{"PC": [0, 1, 2], "RW": [0, 1, 0], "ADDR": [0, 1, 2], "VAL": [0, 0, 0]}
+{"PC": [0, 1, 2], "RW": [0, 0, 1], "ADDR": [0, 1, 2], "VAL": [0, 0, 0]}
+{"PC": [0, 1, 2], "RW": [0, 1, 1], "ADDR": [0, 1, 2], "VAL": [0, 0, 0]}
+{"PC": [0, 1, 2], "RW": [0, 0, 0], "ADDR": [0, 2, 2], "VAL": [0, 0, 0]}
+{"PC": [0, 1, 2], "RW": [0, 1, 0], "ADDR": [0, 2, 2], "VAL": [0, 0, 0]}
+{"PC": [0, 1, 2], "RW": [0, 0, 1], "ADDR": [0, 2, 2], "VAL": [0, 0, 0]}
+{"PC": [0, 1, 2], "RW": [0, 1, 1], "ADDR": [0, 2, 2], "VAL": [0, 0, 0]}
+{"PC": [0, 1, 2], "RW": [0, 1, 1], "ADDR": [0, 0, 0], "VAL": [0, 1, 0]}
+{"PC": [0, 1, 2], "RW": [0, 1, 0], "ADDR": [0, 1, 0], "VAL": [0, 1, 0]}
+{"PC": [0, 1, 2], "RW": [0, 1, 1], "ADDR": [0, 1, 0], "VAL": [0, 1, 0]}
+{"PC": [0, 1, 2], "RW": [0, 1, 0], "ADDR": [0, 2, 0], "VAL": [0, 1, 0]}
+{"PC": [0, 1, 2], "RW": [0, 1, 1], "ADDR": [0, 2, 0], "VAL": [0, 1, 0]}
+{"PC": [0, 1, 2], "RW": [0, 1, 0], "ADDR": [0, 0, 1], "VAL": [0, 1, 0]}
+{"PC": [0, 1, 2], "RW": [0, 1, 1], "ADDR": [0, 0, 1], "VAL": [0, 1, 0]}
+{"PC": [0, 1, 2], "RW": [0, 1, 1], "ADDR": [0, 1, 1], "VAL": [0, 1, 0]}
+{"PC": [0, 1, 2], "RW": [0, 1, 0], "ADDR": [0, 2, 1], "VAL": [0, 1, 0]}
+{"PC": [0, 1, 2], "RW": [0, 1, 1], "ADDR": [0, 2, 1], "VAL": [0, 1, 0]}
+{"PC": [0, 1, 2], "RW": [0, 1, 0], "ADDR": [0, 0, 2], "VAL": [0, 1, 0]}
+{"PC": [0, 1, 2], "RW": [0, 1, 1], "ADDR": [0, 0, 2], "VAL": [0, 1, 0]}
+{"PC": [0, 1, 2], "RW": [0, 1, 0], "ADDR": [0, 1, 2], "VAL": [0, 1, 0]}
+{"PC": [0, 1, 2], "RW": [0, 1, 1], "ADDR": [0, 1, 2], "VAL": [0, 1, 0]}
+{"PC": [0, 1, 2], "RW": [0, 1, 1], "ADDR": [0, 2, 2], "VAL": [0, 1, 0]}
+{"PC": [0, 1, 2], "RW": [0, 1, 1], "ADDR": [0, 0, 0], "VAL": [0, 2, 0]}
+{"PC": [0, 1, 2], "RW": [0, 1, 0], "ADDR": [0, 1, 0], "VAL": [0, 2, 0]}
+{"PC": [0, 1, 2], "RW": [0, 1, 1], "ADDR": [0, 1, 0], "VAL": [0, 2, 0]}
+{"PC": [0, 1, 2], "RW": [0, 1, 0], "ADDR": [0, 2, 0], "VAL": [0, 2, 0]}
+{"PC": [0, 1, 2], "RW": [0, 1, 1], "ADDR": [0, 2, 0], "VAL": [0, 2, 0]}
+{"PC": [0, 1, 2], "RW": [0, 1, 0], "ADDR": [0, 0, 1], "VAL": [0, 2, 0]}
+{"PC": [0, 1, 2], "RW": [0, 1, 1], "ADDR": [0, 0, 1], "VAL": [0, 2, 0]}
+{"PC": [0, 1, 2], "RW": [0, 1, 1], "ADDR": [0, 1, 1], "VAL": [0, 2, 0]}
+{"PC": [0, 1, 2], "RW": [0, 1, 0], "ADDR": [0, 2, 1], "VAL": [0, 2, 0]}
+{"PC": [0, 1, 2], "RW": [0, 1, 1], "ADDR": [0, 2, 1], "VAL": [0, 2, 0]}
+{"PC": [0, 1, 2], "RW": [0, 1, 0], "ADDR": [0, 0, 2], "VAL": [0, 2, 0]}
+{"PC": [0, 1, 2], "RW": [0, 1, 1], "ADDR": [0, 0, 2], "VAL": [0, 2, 0]}
+{"PC": [0, 1, 2], "RW": [0, 1, 0], "ADDR": [0, 1, 2], "VAL": [0, 2, 0]}
+{"PC": [0, 1, 2], "RW": [0, 1, 1], "ADDR": [0, 1, 2], "VAL": [0, 2, 0]}
+{"PC": [0, 1, 2], "RW": [0, 1, 1], "ADDR": [0, 2, 2], "VAL": [0, 2, 0]}
+{"PC": [0, 0, 1], "RW": [0, 0, 1], "ADDR": [0, 0, 0], "VAL": [0, 0, 1]}
+{"PC": [0, 1, 2], "RW": [0, 0, 1], "ADDR": [0, 0, 0], "VAL": [0, 0, 1]}
+{"PC": [0, 1, 2], "RW": [0, 1, 1], "ADDR": [0, 0, 0], "VAL": [0, 0, 1]}
+{"PC": [0, 1, 2], "RW": [0, 0, 1], "ADDR": [0, 1, 0], "VAL": [0, 0, 1]}
+{"PC": [0, 1, 2], "RW": [0, 1, 1], "ADDR": [0, 1, 0], "VAL": [0, 0, 1]}
+{"PC": [0, 1, 2], "RW": [0, 0, 1], "ADDR": [0, 2, 0], "VAL": [0, 0, 1]}
+{"PC": [0, 1, 2], "RW": [0, 1, 1], "ADDR": [0, 2, 0], "VAL": [0, 0, 1]}
+{"PC": [0, 0, 1], "RW": [0, 0, 1], "ADDR": [0, 0, 1], "VAL": [0, 0, 1]}
+{"PC": [0, 1, 2], "RW": [0, 0, 1], "ADDR": [0, 0, 1], "VAL": [0, 0, 1]}
+{"PC": [0, 1, 2], "RW": [0, 1, 1], "ADDR": [0, 0, 1], "VAL": [0, 0, 1]}
+{"PC": [0, 1, 2], "RW": [0, 0, 1], "ADDR": [0, 1, 1], "VAL": [0, 0, 1]}
+{"PC": [0, 1, 2], "RW": [0, 1, 1], "ADDR": [0, 1, 1], "VAL": [0, 0, 1]}
+{"PC": [0, 1, 2], "RW": [0, 0, 1], "ADDR": [0, 2, 1], "VAL": [0, 0, 1]}
+{"PC": [0, 1, 2], "RW": [0, 1, 1], "ADDR": [0, 2, 1], "VAL": [0, 0, 1]}
+{"PC": [0, 0, 1], "RW": [0, 0, 1], "ADDR": [0, 0, 2], "VAL": [0, 0, 1]}
+{"PC": [0, 1, 2], "RW": [0, 0, 1], "ADDR": [0, 0, 2], "VAL": [0, 0, 1]}
+{"PC": [0, 1, 2], "RW": [0, 1, 1], "ADDR": [0, 0, 2], "VAL": [0, 0, 1]}
+{"PC": [0, 1, 2], "RW": [0, 0, 1], "ADDR": [0, 1, 2], "VAL": [0, 0, 1]}
+{"PC": [0, 1, 2], "RW": [0, 1, 1], "ADDR": [0, 1, 2], "VAL": [0, 0, 1]}
+{"PC": [0, 1, 2], "RW": [0, 0, 1], "ADDR": [0, 2, 2], "VAL": [0, 0, 1]}
+{"PC": [0, 1, 2], "RW": [0, 1, 1], "ADDR": [0, 2, 2], "VAL": [0, 0, 1]}
+{"PC": [0, 1, 2], "RW": [0, 1, 0], "ADDR": [0, 0, 0], "VAL": [0, 1, 1]}
+{"PC": [0, 1, 2], "RW": [0, 1, 1], "ADDR": [0, 0, 0], "VAL": [0, 1, 1]}
+{"PC": [0, 1, 2], "RW": [0, 1, 1], "ADDR": [0, 1, 0], "VAL": [0, 1, 1]}
+{"PC": [0, 1, 2], "RW": [0, 1, 1], "ADDR": [0, 2, 0], "VAL": [0, 1, 1]}
+{"PC": [0, 1, 2], "RW": [0, 1, 1], "ADDR": [0, 0, 1], "VAL": [0, 1, 1]}
+{"PC": [0, 1, 2], "RW": [0, 1, 0], "ADDR": [0, 1, 1], "VAL": [0, 1, 1]}
+{"PC": [0, 1, 2], "RW": [0, 1, 1], "ADDR": [0, 1, 1], "VAL": [0, 1, 1]}
+{"PC": [0, 1, 2], "RW": [0, 1, 1], "ADDR": [0, 2, 1], "VAL": [0, 1, 1]}
+{"PC": [0, 1, 2], "RW": [0, 1, 1], "ADDR": [0, 0, 2], "VAL": [0, 1, 1]}
+{"PC": [0, 1, 2], "RW": [0, 1, 1], "ADDR": [0, 1, 2], "VAL": [0, 1, 1]}
+{"PC": [0, 1, 2], "RW": [0, 1, 0], "ADDR": [0, 2, 2], "VAL": [0, 1, 1]}
+{"PC": [0, 1, 2], "RW": [0, 1, 1], "ADDR": [0, 2, 2], "VAL": [0, 1, 1]}
+{"PC": [0, 1, 2], "RW": [0, 1, 1], "ADDR": [0, 0, 0], "VAL": [0, 2, 1]}
+{"PC": [0, 1, 2], "RW": [0, 1, 1], "ADDR": [0, 1, 0], "VAL": [0, 2, 1]}
+{"PC": [0, 1, 2], "RW": [0, 1, 1], "ADDR": [0, 2, 0], "VAL": [0, 2, 1]}
+{"PC": [0, 1, 2], "RW": [0, 1, 1], "ADDR": [0, 0, 1], "VAL": [0, 2, 1]}
+{"PC": [0, 1, 2], "RW": [0, 1, 1], "ADDR": [0, 1, 1], "VAL": [0, 2, 1]}
+{"PC": [0, 1, 2], "RW": [0, 1, 1], "ADDR": [0, 2, 1], "VAL": [0, 2, 1]}
+{"PC": [0, 1, 2], "RW": [0, 1, 1], "ADDR": [0, 0, 2], "VAL": [0, 2, 1]}
+{"PC": [0, 1, 2], "RW": [0, 1, 1], "ADDR": [0, 1, 2], "VAL": [0, 2, 1]}
+{"PC": [0, 1, 2], "RW": [0, 1, 1], "ADDR": [0, 2, 2], "VAL": [0, 2, 1]}
+{"PC": [0, 0, 1], "RW": [0, 0, 1], "ADDR": [0, 0, 0], "VAL": [0, 0, 2]}
+{"PC": [0, 1, 2], "RW": [0, 0, 1], "ADDR": [0, 0, 0], "VAL": [0, 0, 2]}
+{"PC": [0, 1, 2], "RW": [0, 1, 1], "ADDR": [0, 0, 0], "VAL": [0, 0, 2]}
+{"PC": [0, 1, 2], "RW": [0, 0, 1], "ADDR": [0, 1, 0], "VAL": [0, 0, 2]}
+{"PC": [0, 1, 2], "RW": [0, 1, 1], "ADDR": [0, 1, 0], "VAL": [0, 0, 2]}
+{"PC": [0, 1, 2], "RW": [0, 0, 1], "ADDR": [0, 2, 0], "VAL": [0, 0, 2]}
+{"PC": [0, 1, 2], "RW": [0, 1, 1], "ADDR": [0, 2, 0], "VAL": [0, 0, 2]}
+{"PC": [0, 0, 1], "RW": [0, 0, 1], "ADDR": [0, 0, 1], "VAL": [0, 0, 2]}
+{"PC": [0, 1, 2], "RW": [0, 0, 1], "ADDR": [0, 0, 1], "VAL": [0, 0, 2]}
+{"PC": [0, 1, 2], "RW": [0, 1, 1], "ADDR": [0, 0, 1], "VAL": [0, 0, 2]}
+{"PC": [0, 1, 2], "RW": [0, 0, 1], "ADDR": [0, 1, 1], "VAL": [0, 0, 2]}
+{"PC": [0, 1, 2], "RW": [0, 1, 1], "ADDR": [0, 1, 1], "VAL": [0, 0, 2]}
+{"PC": [0, 1, 2], "RW": [0, 0, 1], "ADDR": [0, 2, 1], "VAL": [0, 0, 2]}
+{"PC": [0, 1, 2], "RW": [0, 1, 1], "ADDR": [0, 2, 1], "VAL": [0, 0, 2]}
+{"PC": [0, 0, 1], "RW": [0, 0, 1], "ADDR": [0, 0, 2], "VAL": [0, 0, 2]}
+{"PC": [0, 1, 2], "RW": [0, 0, 1], "ADDR": [0, 0, 2], "VAL": [0, 0, 2]}
+{"PC": [0, 1, 2], "RW": [0, 1, 1], "ADDR": [0, 0, 2], "VAL": [0, 0, 2]}
+{"PC": [0, 1, 2], "RW": [0, 0, 1], "ADDR": [0, 1, 2], "VAL": [0, 0, 2]}
+{"PC": [0, 1, 2], "RW": [0, 1, 1], "ADDR": [0, 1, 2], "VAL": [0, 0, 2]}
+{"PC": [0, 1, 2], "RW": [0, 0, 1], "ADDR": [0, 2, 2], "VAL": [0, 0, 2]}
+{"PC": [0, 1, 2], "RW": [0, 1, 1], "ADDR": [0, 2, 2], "VAL": [0, 0, 2]}
+{"PC": [0, 1, 2], "RW": [0, 1, 1], "ADDR": [0, 0, 0], "VAL": [0, 1, 2]}
+{"PC": [0, 1, 2], "RW": [0, 1, 1], "ADDR": [0, 1, 0], "VAL": [0, 1, 2]}
+{"PC": [0, 1, 2], "RW": [0, 1, 1], "ADDR": [0, 2, 0], "VAL": [0, 1, 2]}
+{"PC": [0, 1, 2], "RW": [0, 1, 1], "ADDR": [0, 0, 1], "VAL": [0, 1, 2]}
+{"PC": [0, 1, 2], "RW": [0, 1, 1], "ADDR": [0, 1, 1], "VAL": [0, 1, 2]}
+{"PC": [0, 1, 2], "RW": [0, 1, 1], "ADDR": [0, 2, 1], "VAL": [0, 1, 2]}
+{"PC": [0, 1, 2], "RW": [0, 1, 1], "ADDR": [0, 0, 2], "VAL": [0, 1, 2]}
+{"PC": [0, 1, 2], "RW": [0, 1, 1], "ADDR": [0, 1, 2], "VAL": [0, 1, 2]}
+{"PC": [0, 1, 2], "RW": [0, 1, 1], "ADDR": [0, 2, 2], "VAL": [0, 1, 2]}
+{"PC": [0, 1, 2], "RW": [0, 1, 0], "ADDR": [0, 0, 0], "VAL": [0, 2, 2]}
+{"PC": [0, 1, 2], "RW": [0, 1, 1], "ADDR": [0, 0, 0], "VAL": [0, 2, 2]}
+{"PC": [0, 1, 2], "RW": [0, 1, 1], "ADDR": [0, 1, 0], "VAL": [0, 2, 2]}
+{"PC": [0, 1, 2], "RW": [0, 1, 1], "ADDR": [0, 2, 0], "VAL": [0, 2, 2]}
+{"PC": [0, 1, 2], "RW": [0, 1, 1], "ADDR": [0, 0, 1], "VAL": [0, 2, 2]}
+{"PC": [0, 1, 2], "RW": [0, 1, 0], "ADDR": [0, 1, 1], "VAL": [0, 2, 2]}
+{"PC": [0, 1, 2], "RW": [0, 1, 1], "ADDR": [0, 1, 1], "VAL": [0, 2, 2]}
+{"PC": [0, 1, 2], "RW": [0, 1, 1], "ADDR": [0, 2, 1], "VAL": [0, 2, 2]}
+{"PC": [0, 1, 2], "RW": [0, 1, 1], "ADDR": [0, 0, 2], "VAL": [0, 2, 2]}
+{"PC": [0, 1, 2], "RW": [0, 1, 1], "ADDR": [0, 1, 2], "VAL": [0, 2, 2]}
+{"PC": [0, 1, 2], "RW": [0, 1, 0], "ADDR": [0, 2, 2], "VAL": [0, 2, 2]}
+{"PC": [0, 1, 2], "RW": [0, 1, 1], "ADDR": [0, 2, 2], "VAL": [0, 2, 2]}
diff --git a/testdata/memory.auto.rejects b/testdata/memory.auto.rejects
new file mode 100644
index 00000000..e911adf2
--- /dev/null
+++ b/testdata/memory.auto.rejects
@@ -0,0 +1,6404 @@
+{"PC": [0, 1, 0], "RW": [0, 0, 0], "ADDR": [0, 0, 0], "VAL": [0, 0, 0]}
+{"PC": [0, 2, 0], "RW": [0, 0, 0], "ADDR": [0, 0, 0], "VAL": [0, 0, 0]}
+{"PC": [0, 1, 1], "RW": [0, 0, 0], "ADDR": [0, 0, 0], "VAL": [0, 0, 0]}
+{"PC": [0, 2, 1], "RW": [0, 0, 0], "ADDR": [0, 0, 0], "VAL": [0, 0, 0]}
+{"PC": [0, 0, 2], "RW": [0, 0, 0], "ADDR": [0, 0, 0], "VAL": [0, 0, 0]}
+{"PC": [0, 2, 2], "RW": [0, 0, 0], "ADDR": [0, 0, 0], "VAL": [0, 0, 0]}
+{"PC": [0, 0, 0], "RW": [0, 1, 0], "ADDR": [0, 0, 0], "VAL": [0, 0, 0]}
+{"PC": [0, 1, 0], "RW": [0, 1, 0], "ADDR": [0, 0, 0], "VAL": [0, 0, 0]}
+{"PC": [0, 2, 0], "RW": [0, 1, 0], "ADDR": [0, 0, 0], "VAL": [0, 0, 0]}
+{"PC": [0, 0, 1], "RW": [0, 1, 0], "ADDR": [0, 0, 0], "VAL": [0, 0, 0]}
+{"PC": [0, 1, 1], "RW": [0, 1, 0], "ADDR": [0, 0, 0], "VAL": [0, 0, 0]}
+{"PC": [0, 2, 1], "RW": [0, 1, 0], "ADDR": [0, 0, 0], "VAL": [0, 0, 0]}
+{"PC": [0, 0, 2], "RW": [0, 1, 0], "ADDR": [0, 0, 0], "VAL": [0, 0, 0]}
+{"PC": [0, 2, 2], "RW": [0, 1, 0], "ADDR": [0, 0, 0], "VAL": [0, 0, 0]}
+{"PC": [0, 0, 0], "RW": [0, 2, 0], "ADDR": [0, 0, 0], "VAL": [0, 0, 0]}
+{"PC": [0, 1, 0], "RW": [0, 2, 0], "ADDR": [0, 0, 0], "VAL": [0, 0, 0]}
+{"PC": [0, 2, 0], "RW": [0, 2, 0], "ADDR": [0, 0, 0], "VAL": [0, 0, 0]}
+{"PC": [0, 0, 1], "RW": [0, 2, 0], "ADDR": [0, 0, 0], "VAL": [0, 0, 0]}
+{"PC": [0, 1, 1], "RW": [0, 2, 0], "ADDR": [0, 0, 0], "VAL": [0, 0, 0]}
+{"PC": [0, 2, 1], "RW": [0, 2, 0], "ADDR": [0, 0, 0], "VAL": [0, 0, 0]}
+{"PC": [0, 0, 2], "RW": [0, 2, 0], "ADDR": [0, 0, 0], "VAL": [0, 0, 0]}
+{"PC": [0, 1, 2], "RW": [0, 2, 0], "ADDR": [0, 0, 0], "VAL": [0, 0, 0]}
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+{"PC": [0, 0, 0], "RW": [0, 0, 1], "ADDR": [0, 0, 0], "VAL": [0, 0, 0]}
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+{"PC": [0, 2, 0], "RW": [0, 0, 1], "ADDR": [0, 0, 0], "VAL": [0, 0, 0]}
+{"PC": [0, 1, 1], "RW": [0, 0, 1], "ADDR": [0, 0, 0], "VAL": [0, 0, 0]}
+{"PC": [0, 2, 1], "RW": [0, 0, 1], "ADDR": [0, 0, 0], "VAL": [0, 0, 0]}
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+{"PC": [0, 2, 2], "RW": [0, 0, 1], "ADDR": [0, 0, 0], "VAL": [0, 0, 0]}
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+{"PC": [0, 1, 0], "RW": [0, 1, 1], "ADDR": [0, 0, 0], "VAL": [0, 0, 0]}
+{"PC": [0, 2, 0], "RW": [0, 1, 1], "ADDR": [0, 0, 0], "VAL": [0, 0, 0]}
+{"PC": [0, 0, 1], "RW": [0, 1, 1], "ADDR": [0, 0, 0], "VAL": [0, 0, 0]}
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+{"PC": [0, 2, 0], "RW": [0, 1, 2], "ADDR": [0, 1, 0], "VAL": [0, 0, 0]}
+{"PC": [0, 0, 1], "RW": [0, 1, 2], "ADDR": [0, 1, 0], "VAL": [0, 0, 0]}
+{"PC": [0, 1, 1], "RW": [0, 1, 2], "ADDR": [0, 1, 0], "VAL": [0, 0, 0]}
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+{"PC": [0, 1, 1], "RW": [0, 2, 2], "ADDR": [0, 1, 0], "VAL": [0, 0, 0]}
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+{"PC": [0, 0, 2], "RW": [0, 2, 2], "ADDR": [0, 1, 0], "VAL": [0, 0, 0]}
+{"PC": [0, 1, 2], "RW": [0, 2, 2], "ADDR": [0, 1, 0], "VAL": [0, 0, 0]}
+{"PC": [0, 2, 2], "RW": [0, 2, 2], "ADDR": [0, 1, 0], "VAL": [0, 0, 0]}
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+{"PC": [0, 1, 0], "RW": [0, 0, 0], "ADDR": [0, 2, 0], "VAL": [0, 0, 0]}
+{"PC": [0, 2, 0], "RW": [0, 0, 0], "ADDR": [0, 2, 0], "VAL": [0, 0, 0]}
+{"PC": [0, 0, 1], "RW": [0, 0, 0], "ADDR": [0, 2, 0], "VAL": [0, 0, 0]}
+{"PC": [0, 1, 1], "RW": [0, 0, 0], "ADDR": [0, 2, 0], "VAL": [0, 0, 0]}
+{"PC": [0, 2, 1], "RW": [0, 0, 0], "ADDR": [0, 2, 0], "VAL": [0, 0, 0]}
+{"PC": [0, 0, 2], "RW": [0, 0, 0], "ADDR": [0, 2, 0], "VAL": [0, 0, 0]}
+{"PC": [0, 2, 2], "RW": [0, 0, 0], "ADDR": [0, 2, 0], "VAL": [0, 0, 0]}
+{"PC": [0, 0, 0], "RW": [0, 1, 0], "ADDR": [0, 2, 0], "VAL": [0, 0, 0]}
+{"PC": [0, 1, 0], "RW": [0, 1, 0], "ADDR": [0, 2, 0], "VAL": [0, 0, 0]}
+{"PC": [0, 2, 0], "RW": [0, 1, 0], "ADDR": [0, 2, 0], "VAL": [0, 0, 0]}
+{"PC": [0, 0, 1], "RW": [0, 1, 0], "ADDR": [0, 2, 0], "VAL": [0, 0, 0]}
+{"PC": [0, 1, 1], "RW": [0, 1, 0], "ADDR": [0, 2, 0], "VAL": [0, 0, 0]}
+{"PC": [0, 2, 1], "RW": [0, 1, 0], "ADDR": [0, 2, 0], "VAL": [0, 0, 0]}
+{"PC": [0, 0, 2], "RW": [0, 1, 0], "ADDR": [0, 2, 0], "VAL": [0, 0, 0]}
+{"PC": [0, 2, 2], "RW": [0, 1, 0], "ADDR": [0, 2, 0], "VAL": [0, 0, 0]}
+{"PC": [0, 0, 0], "RW": [0, 2, 0], "ADDR": [0, 2, 0], "VAL": [0, 0, 0]}
+{"PC": [0, 1, 0], "RW": [0, 2, 0], "ADDR": [0, 2, 0], "VAL": [0, 0, 0]}
+{"PC": [0, 2, 0], "RW": [0, 2, 0], "ADDR": [0, 2, 0], "VAL": [0, 0, 0]}
+{"PC": [0, 0, 1], "RW": [0, 2, 0], "ADDR": [0, 2, 0], "VAL": [0, 0, 0]}
+{"PC": [0, 1, 1], "RW": [0, 2, 0], "ADDR": [0, 2, 0], "VAL": [0, 0, 0]}
+{"PC": [0, 2, 1], "RW": [0, 2, 0], "ADDR": [0, 2, 0], "VAL": [0, 0, 0]}
+{"PC": [0, 0, 2], "RW": [0, 2, 0], "ADDR": [0, 2, 0], "VAL": [0, 0, 0]}
+{"PC": [0, 1, 2], "RW": [0, 2, 0], "ADDR": [0, 2, 0], "VAL": [0, 0, 0]}
+{"PC": [0, 2, 2], "RW": [0, 2, 0], "ADDR": [0, 2, 0], "VAL": [0, 0, 0]}
+{"PC": [0, 0, 0], "RW": [0, 0, 1], "ADDR": [0, 2, 0], "VAL": [0, 0, 0]}
+{"PC": [0, 1, 0], "RW": [0, 0, 1], "ADDR": [0, 2, 0], "VAL": [0, 0, 0]}
+{"PC": [0, 2, 0], "RW": [0, 0, 1], "ADDR": [0, 2, 0], "VAL": [0, 0, 0]}
+{"PC": [0, 0, 1], "RW": [0, 0, 1], "ADDR": [0, 2, 0], "VAL": [0, 0, 0]}
+{"PC": [0, 1, 1], "RW": [0, 0, 1], "ADDR": [0, 2, 0], "VAL": [0, 0, 0]}
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+{"PC": [0, 2, 2], "RW": [0, 0, 2], "ADDR": [0, 2, 2], "VAL": [0, 2, 2]}
+{"PC": [0, 0, 0], "RW": [0, 1, 2], "ADDR": [0, 2, 2], "VAL": [0, 2, 2]}
+{"PC": [0, 1, 0], "RW": [0, 1, 2], "ADDR": [0, 2, 2], "VAL": [0, 2, 2]}
+{"PC": [0, 2, 0], "RW": [0, 1, 2], "ADDR": [0, 2, 2], "VAL": [0, 2, 2]}
+{"PC": [0, 0, 1], "RW": [0, 1, 2], "ADDR": [0, 2, 2], "VAL": [0, 2, 2]}
+{"PC": [0, 1, 1], "RW": [0, 1, 2], "ADDR": [0, 2, 2], "VAL": [0, 2, 2]}
+{"PC": [0, 2, 1], "RW": [0, 1, 2], "ADDR": [0, 2, 2], "VAL": [0, 2, 2]}
+{"PC": [0, 0, 2], "RW": [0, 1, 2], "ADDR": [0, 2, 2], "VAL": [0, 2, 2]}
+{"PC": [0, 1, 2], "RW": [0, 1, 2], "ADDR": [0, 2, 2], "VAL": [0, 2, 2]}
+{"PC": [0, 2, 2], "RW": [0, 1, 2], "ADDR": [0, 2, 2], "VAL": [0, 2, 2]}
+{"PC": [0, 0, 0], "RW": [0, 2, 2], "ADDR": [0, 2, 2], "VAL": [0, 2, 2]}
+{"PC": [0, 1, 0], "RW": [0, 2, 2], "ADDR": [0, 2, 2], "VAL": [0, 2, 2]}
+{"PC": [0, 2, 0], "RW": [0, 2, 2], "ADDR": [0, 2, 2], "VAL": [0, 2, 2]}
+{"PC": [0, 0, 1], "RW": [0, 2, 2], "ADDR": [0, 2, 2], "VAL": [0, 2, 2]}
+{"PC": [0, 1, 1], "RW": [0, 2, 2], "ADDR": [0, 2, 2], "VAL": [0, 2, 2]}
+{"PC": [0, 2, 1], "RW": [0, 2, 2], "ADDR": [0, 2, 2], "VAL": [0, 2, 2]}
+{"PC": [0, 0, 2], "RW": [0, 2, 2], "ADDR": [0, 2, 2], "VAL": [0, 2, 2]}
+{"PC": [0, 1, 2], "RW": [0, 2, 2], "ADDR": [0, 2, 2], "VAL": [0, 2, 2]}
+{"PC": [0, 2, 2], "RW": [0, 2, 2], "ADDR": [0, 2, 2], "VAL": [0, 2, 2]}
diff --git a/testdata/memory.lisp b/testdata/memory.lisp
index 1d96da71..949cd39d 100644
--- a/testdata/memory.lisp
+++ b/testdata/memory.lisp
@@ -20,16 +20,17 @@
 (column VAL :u8)
 ;; Permutation
 (permute (ADDR' PC' RW' VAL') (+ADDR +PC +RW +VAL))
-
 ;; PC[0]=0
 (vanish:first heartbeat_1 PC)
-;; PC[k]=PC[k-1]+1
+;; PC[k]=0 || PC[k]=PC[k-1]+1
 (vanish heartbeat_2 (* PC (- PC (+ 1 (shift PC -1)))))
-
+;; PC[k]=0 ==> PC[k-1]=0
+(vanish heartbeat_3 (if PC (shift PC -1)))
+;; PC[k]=0 ==> (RW[k]=0 && ADDR[k]=0 && VAL[k]=0)
+(vanish heartbeat_4 (if PC (+ RW ADDR VAL)))
 ;; ADDR'[k] != ADDR'[k-1] ==> (RW'[k]=1 || VAL'[k]=0)
 (vanish first_read_1 (ifnot (- ADDR' (shift ADDR' -1)) (* (- 1 RW') VAL')))
 ;; (RW'[0]=1 || VAL'[0]=0)
 (vanish:first first_read_2 (* (- 1 RW') VAL'))
-
 ;; ADDR'[k] == ADDR'[k-1] ==> (RW=1 || VAL'[k]=VAL'[k-1])
 (vanish next_read (if (- ADDR' (shift ADDR' -1)) (* (- 1 RW') (- VAL' (shift VAL' -1)))))