A Kleene algebra with tests for union bound reasoning about probabilistic programs - Archive ouverte HAL
Pré-Publication, Document De Travail (Preprint/Prepublication) Année : 2024

A Kleene algebra with tests for union bound reasoning about probabilistic programs

Résumé

Kleene Algebra with Tests (KAT) provides a framework for algebraic equational reasoning about imperative programs. The recent variant Guarded KAT (GKAT) allows to reason on non-probabilistic properties of probabilistic programs. Here we introduce an extension of this framework called approximate GKAT (aGKAT), which equips GKAT with a partially ordered monoid (real numbers) enabling to express satisfaction of (deterministic) properties \textit{except} with a probability up to a certain bound. This allows to represent in equational reasoning `à la KAT' proofs of probabilistic programs based on the union bound, a technique from basic probability theory. We show how a propositional variant of approximate Hoare Logic (aHL), a program logic for union bound, can be soundly encoded in our system aGKAT. We also show with an example that aGKAT is more general than aHL, in the sense that it can prove some probability bounds that aHL cannot.
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Dates et versions

hal-04196675 , version 1 (05-09-2023)
hal-04196675 , version 2 (29-07-2024)

Identifiants

  • HAL Id : hal-04196675 , version 2

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Leandro Gomes, Patrick Baillot, Marco Gaboardi. A Kleene algebra with tests for union bound reasoning about probabilistic programs. 2024. ⟨hal-04196675v2⟩
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