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Trace abstraction modulo probability

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Aws AlbarghouthiAuthors Info & Claims

Proceedings of the ACM on Programming Languages, Volume 3, Issue POPL

Article No.: 39, Pages 1 - 31

https://doi.org/10.1145/3290352

Published: 02 January 2019 Publication History

Abstract

We propose trace abstraction modulo probability, a proof technique for verifying high-probability accuracy guarantees of probabilistic programs. Our proofs overapproximate the set of program traces using failure automata, finite-state automata that upper bound the probability of failing to satisfy a target specification. We automate proof construction by reducing probabilistic reasoning to logical reasoning: we use program synthesis methods to select axioms for sampling instructions, and then apply Craig interpolation to prove that traces fail the target specification with only a small probability. Our method handles programs with unknown inputs, parameterized distributions, infinite state spaces, and parameterized specifications. We evaluate our technique on a range of randomized algorithms drawn from the differential privacy literature and beyond. To our knowledge, our approach is the first to automatically establish accuracy properties of these algorithms.

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Index Terms

Trace abstraction modulo probability
1. Security and privacy
  1. Security services
    1. Privacy-preserving protocols
2. Theory of computation

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cover image Proceedings of the ACM on Programming Languages

Proceedings of the ACM on Programming Languages Volume 3, Issue POPL

January 2019

2275 pages

EISSN:2475-1421

DOI:10.1145/3302515

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This work is licensed under a Creative Commons Attribution International 4.0 License.

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Association for Computing Machinery

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Published: 02 January 2019

Published in PACMPL Volume 3, Issue POPL

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Bao JTrivedi NPathak DHsu JRoy S(2024)Data-driven invariant learning for probabilistic programsFormal Methods in System Design10.1007/s10703-024-00466-xOnline publication date: 3-Dec-2024
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Sun YFu HChatterjee KGoharshady A(2023)Automated Tail Bound Analysis for Probabilistic Recurrence RelationsComputer Aided Verification10.1007/978-3-031-37709-9_2(16-39)Online publication date: 17-Jul-2023
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