{"uid":"cap_IIlU9s0cnFjStZPkhiYxc","slug":"boolean-gate-basis-functional-completeness-checker-fb0428c1","name":"Boolean Gate Basis Functional Completeness Checker","description":"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.","url":"https://detect.halowerk.com/v1/F-B-NIGHT-FINITE-STRUCTURES/post-boolean-gate-functional-completeness?utm_source=zero.xyz","method":"POST","headers":{},"bodySchema":{"type":"object","properties":{"artifact":{"type":"object","required":["post"],"properties":{"post":{"type":"object","required":["gates","claim"],"properties":{"claim":{"type":"object","required":["gate_classes","blocking_classes","functionally_complete"],"properties":{"gate_classes":{"type":"array","items":{"type":"object","required":["T0","T1","M","S","L"],"properties":{"L":{"type":"boolean"},"M":{"type":"boolean"},"S":{"type":"boolean"},"T0":{"type":"boolean"},"T1":{"type":"boolean"}},"additionalProperties":false},"maxItems":8,"minItems":0},"blocking_classes":{"type":"array","items":{"enum":["T0","T1","M","S","L"]},"maxItems":5,"minItems":0},"functionally_complete":{"type":"boolean"}},"additionalProperties":false},"gates":{"type":"array","items":{"type":"array","items":{"type":"boolean"},"maxItems":16,"minItems":2},"maxItems":8,"minItems":0}},"additionalProperties":false}},"additionalProperties":false}}},"responseSchema":null,"example":null,"exampleRequest":null,"tags":["x402"],"displayCostAmount":"0.003","displayCostAsset":"USDC","priceDynamic":false,"priceHint":null,"priceStatus":"priced","priceSource":"probe","requiresHandshake":false,"reviewCount":0,"rating":{"score":"0.00","successRate":"0.00","reviews":0,"stars":null,"state":"unrated"},"availabilityStatus":"unknown","priceObserved":null,"sessionDeposit":null,"pricing":{"kind":"static","summary":"$0.003/call","primary":{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.003","per":"call","confidence":"exact"},"accepted":[{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.003","per":"call","confidence":"exact"}]},"paymentMethods":[{"uid":"pm_DVEOH9Q7fGsAI1D-W09D9","protocol":"x402","methodType":"crypto","chain":"base","mode":"charge","costAmount":"0.003","costPer":"request","priority":0,"asset":"0x833589fCD6eDb6E08f4c7C32D4f71b54bdA02913","unit":"request","depositMicros":null,"planRef":null}],"brandName":null,"brandSlug":null,"brandBaseUrl":null,"brandDocsUrl":null,"whatItDoes":"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.","exampleAgentPrompt":"Check if this gate basis is functionally complete: I have gates with truth tables [false,false,false,true] (AND), [false,true,true,true] (OR), and [true,false] (NOT) — tell me which of Post's five maximal clones each gate falls into, which clones are blocking, and whether the full set is universal.","exampleUseCases":[{"title":"Logic synthesis toolchain gate validation","prompt":"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?"},{"title":"Formal verification of educational gate set","prompt":"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."},{"title":"Hardware design gate completeness audit","prompt":"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."}],"resultDescription":"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).","failureModes":["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"],"whenToPreferThis":"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.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-11-04T06:39:18.675Z","isFirstParty":false,"canonicalSlug":"boolean-gate-basis-functional-completeness-checker-fb0428c1"}