Random Boolean Formula to CNF Exercise Generator

Description

Generate an exact-operator-count bounded Boolean syntax tree from supplied named variables/operators and delegate Tseitin CNF with named-variable mappings; random choices are conditional on remaining depth capacity, and auxiliary-variable CNF is equisatisfiable rather than the original-variable distributive expansion.

A generated practice exercise contains a prompt and an answer key under a specific rule set. A planted answer establishes one possible solution; only an explicit enumeration or uniqueness check establishes whether alternatives exist.

When to use this tool

Use this generator to create reproducible boolean formula cnf exercise cases from the supplied model or bank. Inspect the returned evidence before using cases in a test or exercise.

How to use the tool and how it works

Supply variableNames, operators, operatorCount, maximumDepth in the field shapes below. Set seed when you need an explicit replay.
Run the tool and correct any input error. For generated controls, distinguish a successful fixture containing an invalid case from failure to generate the fixture.
Read formulaJson, clauses, namedVariables, totalVariableCount. Use the conventions below. Keep answer-bearing fields separate when presenting an exercise.

Construct a Boolean expression tree with exactly operatorCount operations within maximumDepth, drawing only operators and subtree sizes that can fit. Delegate Tseitin CNF conversion and return clauses, named-variable IDs, and the total variable count.^[1]

Delegated operations used for this result: sat to cnf. Their calculation or parsing conventions apply to the corresponding result fields.^[2]

Input field	Meaning and units	Accepted input
variableNames	Variable Names	Required. Array of Text; minimum UTF-16 length 1; maximum UTF-16 length 32.; minimum items 1; maximum items 16.
operators	Operators	Required. Array of Text; one of "not", "and", "or", "implies".; minimum items 1; maximum items 4.
operatorCount	Operator Count	Required. Safe integer; minimum 0; maximum 24.
maximumDepth	Maximum Depth	Required. Safe integer; minimum 1; maximum 12.
seed	Optional numeric seed; takes precedence over context randomness. Without either, use the fixed tool.io default seed.	Optional. Safe integer.

Output field	Interpretation	Returned shape
formulaJson	Formula Json	Required. Text; minimum UTF-16 length 1; maximum UTF-16 length 8192.
clauses	Clauses	Required. Array of Array of Safe integer; minimum -100; maximum 100.; minimum items 1; maximum items 3.; minimum items 1; maximum items 145.
namedVariables	Named Variables	Required. Array of Object; no unknown keys.; minimum items 1; maximum items 16.
namedVariables[].name	Name	Required. Text; minimum UTF-16 length 1; maximum UTF-16 length 32.
namedVariables[].id	Literal identifier used independently of display labels.	Required. Safe integer; minimum 1; maximum 100.
totalVariableCount	Total Variable Count	Required. Safe integer; minimum 1; maximum 100.
randomness	Replay source and normalized 32-bit seed, or null seed for an advancing context source.	Required. Object; no unknown keys.
randomness.seed	Optional safe-integer replay seed; normalization and precedence are explained below.	Required. Safe integer. or Null.
randomness.source	Source	Required. Text; one of "context", "seed".

An explicit safe-integer seed takes precedence over injected context randomness and is normalized to an unsigned 32-bit integer. With no seed and no context source, replay uses the fixed tool.io default seed. A context source must return finite values from zero inclusive to one exclusive; its advancing state must be retained separately. randomness records the source and normalized seed, or null for context. These generators are not cryptographic random sources.

json

{
  "input": {
    "variableNames": [
      "a",
      "b"
    ],
    "operators": [
      "and",
      "not"
    ],
    "operatorCount": 2,
    "maximumDepth": 2,
    "seed": 42
  },
  "output": {
    "formulaJson": "{\"op\":\"not\",\"arg\":{\"op\":\"and\",\"args\":[{\"op\":\"var\",\"name\":\"b\"},{\"op\":\"var\",\"name\":\"a\"}]}}",
    "clauses": [
      [
        -3,
        1
      ],
      [
        -3,
        2
      ],
      [
        3,
        -1,
        -2
      ],
      [
        -4,
        -3
      ],
      [
        4,
        3
      ],
      [
        4
      ]
    ],
    "namedVariables": [
      {
        "name": "b",
        "id": 1
      },
      {
        "name": "a",
        "id": 2
      }
    ],
    "totalVariableCount": 4,
    "randomness": {
      "seed": 42,
      "source": "seed"
    }
  }
}

Limitations and assumptions

Auxiliary variables make the clauses equisatisfiable with the asserted formula under the linked converter, not literally identical in variable space. A variable bank need not have every variable appear; depth and operator work are bounded.
A replay requires the same complete input and implementation. The stated sampling convention applies within its eligible space. A finite draw does not exhaust all possible outputs; repeats remain possible unless a distinct-selection rule is explicit.
The field tables state structural bounds; cross-field constraints and bounded search or output budgets also apply. Unknown keys are rejected where the object contract disallows them. Input errors are distinct from null fields and deliberate invalid controls in a successful output.

Alternative or Complementary methods

For a supplied example, inspect the returned construction or delegated check directly. To evaluate a consumer, also test cases chosen for its own boundaries; a generated finite corpus does not establish exhaustive coverage.

References

Tool behavior and example: Random Boolean Formula to CNF Exercise Generator — tool.io
Calculation or validation: logic/sat-to-cnf — tool.io

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