# Boolean Gate Basis Functional Completeness Checker

> 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.

## Facts

- Endpoint: POST https://detect.halowerk.com/v1/F-B-NIGHT-FINITE-STRUCTURES/post-boolean-gate-functional-completeness?utm_source=zero.xyz
- Price: $0.003/call
- Payment: x402
- Status: unknown
- Last checked: 2026-11-04
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/boolean-gate-basis-functional-completeness-checker-fb0428c1
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_IIlU9s0cnFjStZPkhiYxc

Status and success rate cover calls made through Zero and Zero's own probes. Third-party monitors may report differently.

## How to call it through Zero

Zero handles the 402 payment challenge and records the run. With the Zero CLI installed (`npm i -g @zeroxyz/cli`):

```sh
zero fetch --capability boolean-gate-basis-functional-completeness-checker-fb0428c1 -d '<json body>'
```

Example prompt: 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.

## When to prefer this

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.

## Known failure modes

- 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

## 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).

## Request schema (JSON Schema)

```json
{
 "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
  }
 }
}
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/boolean-gate-basis-functional-completeness-checker-fb0428c1/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from detect.halowerk.com](https://www.zero.xyz/host/detect.halowerk.com/llms.txt)