A Demonic Outcome Logic for Randomized Nondeterminism

Programs increasingly rely on randomization in applications such as cryptography and machine learning. Analyzing randomized programs has been a fruitful research direction, but there is a gap when programs also exploit nondeterminism (for concurrency, efficiency, or algorithmic design). In this pape...

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Veröffentlicht in:Proceedings of ACM on programming languages Jg. 9; H. POPL; S. 539 - 568
Hauptverfasser: Zilberstein, Noam, Kozen, Dexter, Silva, Alexandra, Tassarotti, Joseph
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York, NY, USA ACM 07.01.2025
Schlagworte:
Denotational semantics
Hoare logic
Probabilistic computation
Programming logic
Theory of computation
Demonic Nondeterminism
Program Logics
Probabilistic Programming
ISSN:2475-1421, 2475-1421
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Zusammenfassung:Programs increasingly rely on randomization in applications such as cryptography and machine learning. Analyzing randomized programs has been a fruitful research direction, but there is a gap when programs also exploit nondeterminism (for concurrency, efficiency, or algorithmic design). In this paper, we introduce Demonic Outcome Logic for reasoning about programs that exploit both randomization and nondeterminism. The logic includes several novel features, such as reasoning about multiple executions in tandem and manipulating pre- and postconditions using familiar equational laws—including the distributive law of probabilistic choices over nondeterministic ones. We also give rules for loops that both establish termination and quantify the distribution of final outcomes from a single premise. We illustrate the reasoning capabilities of Demonic Outcome Logic through several case studies, including the Monty Hall problem, an adversarial protocol for simulating fair coins, and a heuristic based probabilistic SAT solver.
ISSN:2475-1421
2475-1421
DOI:10.1145/3704855