Source: https://guthlabs.ai/docs/instruments/boolean-logic-truth-table-generator/mechanism/

instrument mechanism / verified-clean

# Boolean Logic Truth Table Generator mechanism

The inspectable method record for Boolean Logic Truth Table Generator, kept separate from implementation and qualification.

Status: **VERIFIED_CLEAN**Lifecycle: **verified-clean**

## Model scope

The Boolean evaluation method is mathematically standard, but the instrument needs a documented grammar and output conventions before it can receive an unconditional PASS. The honest label is currently empty; it should state that simplified SOP output may be non-unique unless minimality and tie-breaking are guaranteed.

- Exhaustive evaluation over 2^n combinations is the standard and correct method for generating a truth table.

- The expression grammar is underspecified: operator precedence, associativity, parentheses, literal constants such as 0 and 1, and accepted token spellings are not defined.

- Minterm and maxterm numbering conventions are unspecified; the vectors below assume the listed variable order is most-significant to least-significant in binary row order.

- Karnaugh-map-style simplification is not a uniquely defined formula unless the tool specifies whether it returns a minimal SOP, one valid SOP, how ties are resolved, and how optional don't-care terms are handled.

- The specification does not state whether duplicate variables, undeclared variables, missing variables, malformed expressions, or an empty variable list are accepted.

## Units and conventions

- Boolean values are dimensionless and represented as false/true or 0/1.

- Truth-table rows are ordered lexicographically with false before true, equivalent to counting the listed variables as a binary number.

- For minterms, variable 1 in the supplied variable list is the most-significant bit; maxterm indices use the same row numbering.

- NOT, AND, OR, XOR, NAND, and NOR are assumed to have their standard Boolean definitions.

## Inspectable vector

One of 4 source-bound review vectors:

````
{
  "inputs": {
    "expression": "NOT A",
    "variables": [
      "A"
    ]
  },
  "expected_outputs": {
    "truth_table": [
      {
        "A": false,
        "output": true
      },
      {
        "A": true,
        "output": false
      }
    ],
    "minterms": [
      0
    ],
    "maxterms": [
      1
    ],
    "simplified_SOP": "NOT A"
  },
  "working": "There are 2^1 = 2 rows. Row 0: A=0, so NOT A = NOT 0 = 1. Row 1: A=1, so NOT A = NOT 1 = 0. Therefore the output column is [1,0]. The true row is binary 0, so minterms = {0}; the false row is binary 1, so maxterms = {1}. The SOP is NOT A."
}
````

## Failure boundary

- There are no physical units and no division-by-zero hazard in Boolean evaluation.

- A variable limit of approximately six must be enforced explicitly: 2^6 = 64 rows, while larger inputs grow exponentially.

- Duplicate variable names can make row generation and minterm numbering ambiguous; they should be rejected or normalized with a documented rule.

- Undeclared variables, malformed syntax, unmatched parentheses, and ambiguous operator precedence require deterministic parse errors rather than silent evaluation.

- NAND and NOR must be parsed with explicit operand grouping; implicit precedence can change the expression's meaning.

- The simplifier must preserve constants correctly: a contradiction has an empty minterm set and SOP 0, while a tautology has an empty maxterm set and SOP 1.

- If K-map grouping is advertised, the implementation must document variable ordering, adjacency rules, treatment of don't-care terms, and whether minimality is guaranteed.

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/boolean-logic-truth-table-generator/>)[03**Implementation**](<https://guthlabs.ai/docs/instruments/boolean-logic-truth-table-generator/implementation/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/boolean-logic-truth-table-generator/qualification/>)

## 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`