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Rational Labelled Markov Chain Probabilistic Bisimulation
x402
Rational Labelled Markov Chain Probabilistic Bisimulation 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).
Computes exact probabilistic bisimilarity classes and the quotient transition matrix for a supplied finite labelled rational Markov chain.
Price / call$0.003
Success—
StatusUnknown
How this service works
A stochastic-model test agent needs exact probabilistic bisimilarity classes and the quotient transition matrix of a supplied finite labelled rational Markov chain, not one target reachability probability or deterministic-automaton language equivalence.
Output
Returns the exact probabilistic bisimilarity equivalence classes (partition of states) and the quotient transition matrix of the supplied rational labelled Markov chain, enabling state-space minimization and formal verification of stochastic models.
Example use cases
Stochastic model minimization check
“I'm testing a 5-state rational Markov chain with labels [0,1,0,1,2], denominator 10, and weights [[3,2,0,5,0],[0,4,3,0,3],[2,0,3,5,0],[0,3,0,4,3],[1,1,2,2,4]]. My claim is that states 0 and 2 fall in the same bisimilarity class — please give me the exact bisimilarity partition and the quotient transition matrix.”
Formal verification of probabilistic equivalence
“For my formal verification pipeline, I need to know the exact probabilistic bisimilarity classes of a 3-state labelled Markov chain with labels [1,2,1], denominator 4, and transition weights [[2,1,1],[1,2,1],[1,1,2]]. No claim states to check — just give me all bisimilarity classes and the quotient matrix.”
Stochastic agent bisimulation correctness test
“My stochastic test agent needs to validate its bisimulation claim: for a Markov chain with labels [0,0,1,1], denominator 8, weights [[4,2,1,1],[3,3,1,1],[1,1,3,3],[1,1,2,4]], and claim [0,1], compute the exact probabilistic bisimilarity classes and confirm whether states 0 and 1 belong to the same class.”
Technical details
Endpoint
POSThttps://detect.halowerk.com/v1/F-NIGHT-ECMA/rational-labelled-markov-probabilistic-bisimulation?utm_source=zero.xyzWhen to prefer
Choose this endpoint when you need exact, symbolic probabilistic bisimilarity computation (not approximation) for a small finite rational Markov chain (up to 16 states). It is specifically suited for stochastic model testing, formal verification pipelines, and quotient reduction tasks — not for single reachability queries or deterministic automaton language equivalence checks.
Side effects
- Weights matrix dimensions inconsistent with labels array length — rejected with validation error
- Denominator value outside allowed range (1–1000) — schema validation failure
- Claim indices reference out-of-range state indices (>15) — rejected
- Transition weights do not form a valid stochastic matrix under the given denominator — computation error
- Malformed or empty labels array — schema rejection
Input
Schema · Request body
| Field | Type | Description |
|---|---|---|
| artifact | object |
Tags
x402
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