Boolean Expression Simplifier (Karnaugh Map) mechanism

Model scope

The core Quine-McCluskey approach is mathematically appropriate for Boolean minimization, but the empty honest_label and the unspecified variable ordering, POS procedure, tie-breaking definition, and don't-care semantics prevent an unconditional PASS.

• Quine-McCluskey is a standard method for generating prime implicants and obtaining a minimal SOP, but the specification does not state that the prime-implicant chart and a covering method such as Petrick's method are used when essential implicants alone do not produce a cover.
• The claimed minimal SOP/POS output is underspecified: it must define whether minimal means fewest product/sum terms, fewest literals, or a lexicographic tie-break among equally minimal results.
• POS minimization requires an explicit procedure, such as applying Quine-McCluskey to the zero-set/maxterms or minimizing the complemented function and applying De Morgan's law; this is not stated.
• The K-map output requires a defined variable ordering and Gray-code row/column ordering; otherwise the visualization is ambiguous.
• Handling of don't-care conditions is not specified, although they materially affect Quine-McCluskey grouping and the resulting minimum expression.

Units and conventions

• Boolean values are unitless and are represented as 0=false and 1=true.
• Minterm numbering assumes the listed variables are ordered left to right with the first variable as the most-significant bit and the last variable as the least-significant bit.
• K-map rows and columns use Gray-code order; the expected grids below state their row and column labels explicitly.
• A prime mark denotes Boolean complement, + denotes OR, and juxtaposition denotes AND.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "variables": [
      "A",
      "B"
    ],
    "minterms": [
      1,
      2,
      3
    ],
    "dont_cares": [],
    "minterm_order": "A is MSB; B is LSB",
    "kmap_order": {
      "rows": "A=0,1",
      "columns": "B=0,1"
    }
  },
  "expected_outputs": {
    "minimal_sop": "A + B",
    "minimal_pos": "(A + B)",
    "kmap_grid": {
      "row_labels": [
        "A=0",
        "A=1"
      ],
      "column_labels": [
        "B=0",
        "B=1"
      ],
      "values": [
        [
          0,
          1
        ],
        [
          1,
          1
        ]
      ]
    },
    "spot_checks": {
      "A=0,B=1": 1,
      "A=1,B=0": 1,
      "A=0,B=0": 0
    }
  },
  "working": "Minterms in binary: 1=01, 2=10, 3=11. Combine 01 with 11: the A bit changes, giving -1 = B. Combine 10 with 11: the B bit changes, giving 1- = A. Minterm 1 is covered only by B, and minterm 2 is covered only by A, so both implicants are essential. Therefore SOP = A + B. The zero-set is only minterm 0 (00), so the minimal POS is the maxterm (A+B). Spot checks: A=0,B=1 gives 0+1=1; A=1,B=0 gives 1+0=1; A=0,B=0 gives 0+0=0."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

The specification does not state a variable bit-order convention, so minterm 1 for variables A and B can legitimately simplify to either A'B or AB'. In addition, a 32-bit signed or bitwise JavaScript implementation can mishandle minterm 4,294,967,295 by converting it to -1, even though the exact mathematical result is a 32-literal product.

Other records

Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

• VERIFIED_LEDGER.json
• evidence-tranche6/tranche6-results.json
• BOUNDARY_HAZARD_CATALOG.json