A Kleene algebra with tests for union bound reasoning about probabilistic programs
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| Titel: | A Kleene algebra with tests for union bound reasoning about probabilistic programs |
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| Autoren: | Gomes, Leandro, Baillot, Patrick, Gaboardi, Marco |
| Weitere Verfasser: | Gomes, Leandro, Leandro Gomes and Patrick Baillot and Marco Gaboardi |
| Verlagsinformationen: | Array, 2025. |
| Publikationsjahr: | 2025 |
| Schlagwörter: | union bound, Kleene algebras with tests Hoare logic equational reasoning probabilistic programs union bound formal verification, Theory of computation → Hoare logic, Hoare logic, equational reasoning, [INFO] Computer Science [cs], Theory of computation → Logic and verification, Theory of computation → Algebraic semantics, Kleene algebras with tests, probabilistic programs, ddc:004, formal verification, Theory of computation → Pre- and post-conditions |
| Beschreibung: | 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 except with a probability up to a certain bound. This allows to represent in equational reasoning ` a 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 then illustrate the use of aGKAT with an example of accuracy analysis from the field of differential privacy. |
| Publikationsart: | Conference object Article |
| Dateibeschreibung: | application/pdf |
| Sprache: | English |
| DOI: | 10.4230/lipics.csl.2025.35 |
| Zugangs-URL: | https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2025.35 |
| Rights: | CC BY |
| Dokumentencode: | edsair.dedup.wf.002..a48c47eb52a13a33ecec27824b4a671f |
| Datenbank: | OpenAIRE |
Nájsť tento článok vo Web of Science | Abstract: | 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 except with a probability up to a certain bound. This allows to represent in equational reasoning ` a 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 then illustrate the use of aGKAT with an example of accuracy analysis from the field of differential privacy. |
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| DOI: | 10.4230/lipics.csl.2025.35 |