Random Binary Constraint Satisfaction Instance Generator

Description

Generate a finite-domain binary extensional CSP with distinct variable pairs and a planted satisfying assignment; other tuples are independently included, without uniqueness or hardness claims.

An optimization instance defines choices, constraints, and an objective. A feasible witness demonstrates that its stated constraints can be met; it establishes optimality only when the tool actually computes and verifies an optimum.

Generate a finite-domain binary extensional CSP with distinct variable pairs and a planted satisfying assignment; other tuples are independently included, without uniqueness or hardness claims.

When to use this tool

Use this generator to create reproducible constraint satisfaction instance 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 variableCount, domainSize, constraintCount, allowedTupleProbability 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 variables, domain, constraints, satisfyingAssignment. Use the conventions below. Keep answer-bearing fields separate when presenting an exercise.

Draw a satisfying assignment, sample distinct unordered variable pairs, and build allowed domain tuples for each pair. Always include the planted assignment's tuple and independently include other tuples under allowedTupleProbability.^[1]

Input field	Meaning and units	Accepted input
variableCount	Variable Count	Required. Safe integer; minimum 2; maximum 32.
domainSize	Domain Size	Required. Safe integer; minimum 1; maximum 16.
constraintCount	Constraint Count	Required. Safe integer; minimum 0; maximum 128.
allowedTupleProbability	Allowed Tuple Probability	Required. Finite number; minimum 0; maximum 1.
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
variables	Variables	Required. Array of Safe integer; minimum 0; maximum 31.; minimum items 2; maximum items 32.
domain	Domain	Required. Array of Safe integer; minimum 0; maximum 15.; minimum items 1; maximum items 16.
constraints	Constraints	Required. Array of Object; no unknown keys.; maximum items 128.
constraints[].variables	Variables	Required. Array of Safe integer; minimum 0; maximum 31.; minimum items 2; maximum items 2.
constraints[].allowedTuples	Allowed Tuples	Required. Array of Array of Safe integer; minimum 0; maximum 31.; minimum items 2; maximum items 2.; minimum items 1; maximum items 256.
satisfyingAssignment	Satisfying Assignment	Required. Array of Safe integer; minimum 0; maximum 15.; minimum items 2; maximum items 32.
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": {
    "variableCount": 4,
    "domainSize": 3,
    "constraintCount": 3,
    "allowedTupleProbability": 0.2,
    "seed": 42
  },
  "output": {
    "variables": [
      0,
      1,
      2,
      3
    ],
    "domain": [
      0,
      1,
      2
    ],
    "constraints": [
      {
        "variables": [
          0,
          1
        ],
        "allowedTuples": [
          [
            1,
            1
          ],
          [
            2,
            0
          ]
        ]
      },
      {
        "variables": [
          1,
          3
        ],
        "allowedTuples": [
          [
            0,
            1
          ],
          [
            1,
            1
          ],
          [
            1,
            2
          ],
          [
            2,
            1
          ]
        ]
      },
      {
        "variables": [
          1,
          2
        ],
        "allowedTuples": [
          [
            0,
            0
          ],
          [
            0,
            1
          ],
          [
            1,
            1
          ],
          [
            1,
            2
          ],
          [
            2,
            0
          ]
        ]
      }
    ],
    "satisfyingAssignment": [
      1,
      1,
      2,
      2
    ],
    "randomness": {
      "seed": 42,
      "source": "seed"
    }
  }
}

Limitations and assumptions

The witness proves feasibility but need not be unique. Tuple orientation follows the returned variable pair order. This does not solve arbitrary constraint instances or control difficulty solely through the inclusion probability.
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 Binary Constraint Satisfaction Instance Generator — tool.io

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