FAILURE MAP
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FA-89161 / Digital logic simulation / Open access

Term positions read least-significant first · case 01

Hazard pairs are reported on mirrored minterm numbers.

Verified by executionVariant 1 · 8 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

Character k of a term is matched against bit k from the LSB instead of from the MSB.

THE FAILURE

Character k of a term is matched against bit k from the LSB instead of from the MSB.

Unsuccessful approach: Off-by-one MSB indexing shifts every variable by one position.

Case contract

Input [nv, terms]: product terms are strings over '0','1','-' with character 0 the most significant variable. Minterm m is covered by a term when every non-'-' position matches bit (m >> (nv-1-k)) & 1. A static-1 hazard is a pair of adjacent minterms (differing in one bit), both in the on-set, that no single term covers together. Return sorted [low, high] pairs.

Why this case matters

Glitch analysis in logic simulators flags transitions that may pulse when two product terms hand off.

1 / The failure

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(*args):
    nv, terms = args
    def covers(t, m):
        for k, ch in enumerate(t):
            bit = (m >> k) & 1
            if ch != '-' and int(ch) != bit:
                return False
        return True
    ones = [m for m in range(2 ** nv) if any(covers(t, m) for t in terms)]
    out = []
    for m in ones:
        for k in range(nv):
            p = m ^ (1 << k)
            if p > m and p in ones and not any(covers(t, m) and covers(t, p) for t in terms):
                out.append([m, p])
    return sorted(out)
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('cover 0', [3, ['1-0', '-11', '11-']], []), ('cover 1', [2, ['1-', '-1']], []), ('cover 2', [4, ['1--0', '-1-1', '0-1-']], [[2, 10], [6, 14], [12, 13], [14, 15]]), ('cover 3', [3, ['0-0', '1-1']], []), ('cover 4', [4, ['11--', '--11']], []), ('cover 5', [3, ['00-', '-01', '1-1']], []), ('cover 6', [4, ['0--1', '-10-', '1-1-']], [[3, 11], [7, 15], [12, 14], [13, 15]]), ('msb only term', [3, ['1--', '0-1']], [[1, 5], [3, 7]])], [('cover 0', [2, ['1-', '-1']], []), ('cover 1', [4, ['1--0', '-1-1', '0-1-']], [[2, 10], [6, 14], [12, 13], [14, 15]]), ('cover 2', [3, ['0-0', '1-1']], []), ('cover 3', [4, ['11--', '--11']], []), ('cover 4', [3, ['00-', '-01', '1-1']], []), ('cover 5', [4, ['0--1', '-10-', '1-1-']], [[3, 11], [7, 15], [12, 14], [13, 15]]), ('cover 6', [3, ['1--', '-1-']], []), ('msb only term', [3, ['1--', '0-1']], [[1, 5], [3, 7]])], [('cover 0', [4, ['1--0', '-1-1', '0-1-']], [[2, 10], [6, 14], [12, 13], [14, 15]]), ('cover 1', [3, ['0-0', '1-1']], []), ('cover 2', [4, ['11--', '--11']], []), ('cover 3', [3, ['00-', '-01', '1-1']], []), ('cover 4', [4, ['0--1', '-10-', '1-1-']], [[3, 11], [7, 15], [12, 14], [13, 15]]), ('cover 5', [3, ['1--', '-1-']], []), ('cover 6', [4, ['1-00', '0-11', '-1-1', '10--']], [[3, 11], [9, 13], [11, 15], [12, 13]]), ('msb only term', [3, ['1--', '0-1']], [[1, 5], [3, 7]])], [('cover 0', [3, ['0-0', '1-1']], []), ('cover 1', [4, ['11--', '--11']], []), ('cover 2', [3, ['00-', '-01', '1-1']], []), ('cover 3', [4, ['0--1', '-10-', '1-1-']], [[3, 11], [7, 15], [12, 14], [13, 15]]), ('cover 4', [3, ['1--', '-1-']], []), ('cover 5', [4, ['1-00', '0-11', '-1-1', '10--']], [[3, 11], [9, 13], [11, 15], [12, 13]]), ('cover 6', [3, ['10-', '-11']], [[5, 7]]), ('msb only term', [3, ['1--', '0-1']], [[1, 5], [3, 7]])], [('cover 0', [4, ['11--', '--11']], []), ('cover 1', [3, ['00-', '-01', '1-1']], []), ('cover 2', [4, ['0--1', '-10-', '1-1-']], [[3, 11], [7, 15], [12, 14], [13, 15]]), ('cover 3', [3, ['1--', '-1-']], []), ('cover 4', [4, ['1-00', '0-11', '-1-1', '10--']], [[3, 11], [9, 13], [11, 15], [12, 13]]), ('cover 5', [3, ['10-', '-11']], [[5, 7]]), ('cover 6', [3, ['1-0', '-11', '11-']], []), ('msb only term', [3, ['1--', '0-1']], [[1, 5], [3, 7]])]]
for label, args, expected in fixtures[N-1]:
    check(label, solve(*args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
Boundary fixtureActualExpectedOutcome
cover 0[][]Passed
cover 1[][]Passed
cover 2[[3, 11], [4, 5], [6, 7], [7, 15]][[2, 10], [6, 14], [12, 13], [14, 15]]Failed
cover 3[][]Passed
cover 4[][]Passed
cover 5[][]Passed
cover 6[[3, 7], [11, 15], [12, 13], [14, 15]][[3, 11], [7, 15], [12, 14], [13, 15]]Failed
msb only term[[4, 5], [6, 7]][[1, 5], [3, 7]]Failed

SHA-256 / 9ea6436093234fce90464ec48e5304bda74b9dc71dcc33e0cb9580ad87dd4ac7

2 / The unsuccessful fix

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(*args):
    nv, terms = args
    def covers(t, m):
        for k, ch in enumerate(t):
            bit = (m >> (nv - k)) & 1
            if ch != '-' and int(ch) != bit:
                return False
        return True
    ones = [m for m in range(2 ** nv) if any(covers(t, m) for t in terms)]
    out = []
    for m in ones:
        for k in range(nv):
            p = m ^ (1 << k)
            if p > m and p in ones and not any(covers(t, m) and covers(t, p) for t in terms):
                out.append([m, p])
    return sorted(out)
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('cover 0', [3, ['1-0', '-11', '11-']], []), ('cover 1', [2, ['1-', '-1']], []), ('cover 2', [4, ['1--0', '-1-1', '0-1-']], [[2, 10], [6, 14], [12, 13], [14, 15]]), ('cover 3', [3, ['0-0', '1-1']], []), ('cover 4', [4, ['11--', '--11']], []), ('cover 5', [3, ['00-', '-01', '1-1']], []), ('cover 6', [4, ['0--1', '-10-', '1-1-']], [[3, 11], [7, 15], [12, 14], [13, 15]]), ('msb only term', [3, ['1--', '0-1']], [[1, 5], [3, 7]])], [('cover 0', [2, ['1-', '-1']], []), ('cover 1', [4, ['1--0', '-1-1', '0-1-']], [[2, 10], [6, 14], [12, 13], [14, 15]]), ('cover 2', [3, ['0-0', '1-1']], []), ('cover 3', [4, ['11--', '--11']], []), ('cover 4', [3, ['00-', '-01', '1-1']], []), ('cover 5', [4, ['0--1', '-10-', '1-1-']], [[3, 11], [7, 15], [12, 14], [13, 15]]), ('cover 6', [3, ['1--', '-1-']], []), ('msb only term', [3, ['1--', '0-1']], [[1, 5], [3, 7]])], [('cover 0', [4, ['1--0', '-1-1', '0-1-']], [[2, 10], [6, 14], [12, 13], [14, 15]]), ('cover 1', [3, ['0-0', '1-1']], []), ('cover 2', [4, ['11--', '--11']], []), ('cover 3', [3, ['00-', '-01', '1-1']], []), ('cover 4', [4, ['0--1', '-10-', '1-1-']], [[3, 11], [7, 15], [12, 14], [13, 15]]), ('cover 5', [3, ['1--', '-1-']], []), ('cover 6', [4, ['1-00', '0-11', '-1-1', '10--']], [[3, 11], [9, 13], [11, 15], [12, 13]]), ('msb only term', [3, ['1--', '0-1']], [[1, 5], [3, 7]])], [('cover 0', [3, ['0-0', '1-1']], []), ('cover 1', [4, ['11--', '--11']], []), ('cover 2', [3, ['00-', '-01', '1-1']], []), ('cover 3', [4, ['0--1', '-10-', '1-1-']], [[3, 11], [7, 15], [12, 14], [13, 15]]), ('cover 4', [3, ['1--', '-1-']], []), ('cover 5', [4, ['1-00', '0-11', '-1-1', '10--']], [[3, 11], [9, 13], [11, 15], [12, 13]]), ('cover 6', [3, ['10-', '-11']], [[5, 7]]), ('msb only term', [3, ['1--', '0-1']], [[1, 5], [3, 7]])], [('cover 0', [4, ['11--', '--11']], []), ('cover 1', [3, ['00-', '-01', '1-1']], []), ('cover 2', [4, ['0--1', '-10-', '1-1-']], [[3, 11], [7, 15], [12, 14], [13, 15]]), ('cover 3', [3, ['1--', '-1-']], []), ('cover 4', [4, ['1-00', '0-11', '-1-1', '10--']], [[3, 11], [9, 13], [11, 15], [12, 13]]), ('cover 5', [3, ['10-', '-11']], [[5, 7]]), ('cover 6', [3, ['1-0', '-11', '11-']], []), ('msb only term', [3, ['1--', '0-1']], [[1, 5], [3, 7]])]]
for label, args, expected in fixtures[N-1]:
    check(label, solve(*args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
Boundary fixtureActualExpectedOutcome
cover 0[][]Passed
cover 1[][]Passed
cover 2[][[2, 10], [6, 14], [12, 13], [14, 15]]Failed
cover 3[][]Passed
cover 4[][]Passed
cover 5[][]Passed
cover 6[][[3, 11], [7, 15], [12, 14], [13, 15]]Failed
msb only term[][[1, 5], [3, 7]]Failed

SHA-256 / 7dd604ad278c1067f51374ed9eb67b256bf5e860b30cc49fc88619973f84325f

HELD IN THE MEMBER ARCHIVE

The verified repair and its recorded checks are member-only.

This mechanism has 8 recorded checks per implementation. The open-access tier publishes the failure and the unsuccessful fix; the repaired source that passes every check, and the observations that prove it, are available to members.

Every case sharing this mechanism uses the same contract and the same repair, so this one record is held back for all of them.

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Verification & scope

A deterministic bounded teaching model of one simulator rule set; the contract is stipulated and is not a claim of conformance to any HDL standard or commercial simulator. This reproducer isolates one failure mechanism. Results cover the supplied fixtures. Variants within a family share a test contract and should remain grouped when constructing evaluation splits. Related mechanisms with a shared evaluation_group must also remain together; these controlled models are not independent production incidents.

Observations recorded using Python 3.12.14 at 2026-09-29T14:51:14.901885+00:00.

Case digest / 6892e8ba16bb0cfd62b8050bc8431e9cd043305a744cb5d24ae33498bf6ffc70