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Boolean Gate Basis Functional Completeness Checker
x402
Boolean Gate Basis Functional Completeness Checker is a paid API for AI agents from detect.halowerk.com, paid per call via x402, $0.003/call, status unknown (last checked 2026-11-04).
Certifies whether a supplied finite gate basis is functionally complete by identifying which of Post's five maximal clones (T0, T1, M, S, L) block universality.
Price / call$0.003
Success—
StatusUnknown
How this service works
A logic-synthesis test agent needs an exact expressiveness certificate for a supplied entire finite gatebasis,including which ofPostsfive maximal clones block universality. Not evaluatingoneformula or measuringBooleanfunctionnonlinearity.
Output
Returns a structured certificate containing: per-gate membership flags for each of Post's five maximal clones (T0, T1, M, S, L), a list of which clones are blocking universality, and a boolean verdict on whether the supplied gate basis is functionally complete (universal).
Example use cases
Logic synthesis toolchain gate validation
“I'm building a logic synthesizer with a custom gate library using only NAND and XNOR. Can you tell me if that gate basis is functionally complete, and which of Post's maximal clones — T0, T1, M, S, or L — are blocking universality if it isn't?”
Formal verification of educational gate set
“For a teaching exercise I defined a gate basis of AND, OR, and XOR — their truth tables are [F,F,F,T], [F,T,T,T], and [F,T,T,F]. Run the Post clone analysis and give me the expressiveness certificate showing whether this basis is universal and what's blocking it if not.”
Hardware design gate completeness audit
“I'm auditing a hardware description where the only allowed primitives are majority-3 and constant-0. Please classify each gate's membership across all five of Post's maximal clones, list any blocking classes, and confirm whether the basis achieves functional completeness.”
Technical details
Endpoint
POSThttps://detect.halowerk.com/v1/F-B-NIGHT-FINITE-STRUCTURES/post-boolean-gate-functional-completeness?utm_source=zero.xyzWhen to prefer
Use this endpoint when you need an exact, formal expressiveness certificate for an entire finite Boolean gate basis against Post's lattice — not when you want to evaluate a single formula, measure nonlinearity, or perform circuit minimization. Ideal for logic synthesis toolchains, formal verification pipelines, and educational tools that need a rigorous clone-theoretic completeness verdict rather than empirical or heuristic checks.
Side effects
- Malformed truth table lengths (not a power of 2 between 2 and 16) cause validation error
- Gate array exceeding 8 gates rejected
- Mismatch between supplied claim and computed result returned as failed verification
- Empty gate basis treated as non-complete with all five clones listed as blocking
- Inconsistent claim fields (e.g. functionally_complete true but blocking_classes non-empty) may cause rejection
Input
Schema · Request body
| Field | Type | Description |
|---|---|---|
| artifact | object |
Tags
x402
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