Article

Does a Program Yield the Right Distribution?: Verifying Probabilistic Programs via Generating Functions

Authors:

Mingshuai Chen,

Joost-Pieter Katoen,

Lutz Klinkenberg,

Tobias WinklerAuthors Info & Claims

Computer Aided Verification: 34th International Conference, CAV 2022, Haifa, Israel, August 7–10, 2022, Proceedings, Part I

Pages 79 - 101

https://doi.org/10.1007/978-3-031-13185-1_5

Published: 07 August 2022 Publication History

Abstract

We study discrete probabilistic programs with potentially unbounded looping behaviors over an infinite state space. We present, to the best of our knowledge, the first decidability result for the problem of determining whether such a program generates exactly a specified distribution over its outputs (provided the program terminates almost-surely). The class of distributions that can be specified in our formalism consists of standard distributions (geometric, uniform, etc.) and finite convolutions thereof. Our method relies on representing these (possibly infinite-support) distributions as probability generating functions which admit effective arithmetic operations. We have automated our techniques in a tool called

P R O D I G Y

, which supports automatic invariance checking, compositional reasoning of nested loops, and efficient queries to the output distribution, as demonstrated by experiments.

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Klinkenberg LBlumenthal CChen MHaase DKatoen J(2024)Exact Bayesian Inference for Loopy Probabilistic Programs using Generating FunctionsProceedings of the ACM on Programming Languages10.1145/36498448:OOPSLA1(923-953)Online publication date: 29-Apr-2024
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cover image Guide Proceedings

Computer Aided Verification: 34th International Conference, CAV 2022, Haifa, Israel, August 7–10, 2022, Proceedings, Part I

Aug 2022

562 pages

ISBN:978-3-031-13184-4

DOI:10.1007/978-3-031-13185-1

Editors:
Sharon Shoham
Tel Aviv University, Tel Aviv, Israel
,
Yakir Vizel
Technion – Israel Institute of Technology, Haifa, Israel

© The Author(s) 2022.

Open Access This chapter is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.The images or other third party material in this chapter are included in the chapter's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the chapter's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.

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Publication History

Published: 07 August 2022

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Cited By

Różowski WSilva ASobocinski PLago UEsparza J(2024)A Completeness Theorem for Probabilistic Regular ExpressionsProceedings of the 39th Annual ACM/IEEE Symposium on Logic in Computer Science10.1145/3661814.3662084(1-14)Online publication date: 8-Jul-2024
https://dl.acm.org/doi/10.1145/3661814.3662084
Klinkenberg LBlumenthal CChen MHaase DKatoen J(2024)Exact Bayesian Inference for Loopy Probabilistic Programs using Generating FunctionsProceedings of the ACM on Programming Languages10.1145/36498448:OOPSLA1(923-953)Online publication date: 29-Apr-2024
https://dl.acm.org/doi/10.1145/3649844
Elsayed-Aly IParker DFeng L(2024)Distributional Probabilistic Model CheckingNASA Formal Methods10.1007/978-3-031-60698-4_4(57-75)Online publication date: 4-Jun-2024
https://dl.acm.org/doi/10.1007/978-3-031-60698-4_4
Zaiser FMurawski AOng COh ANaumann TGloberson ASaenko KHardt MLevine S(2023)Exact Bayesian inference on discrete models via probability generating functionsProceedings of the 37th International Conference on Neural Information Processing Systems10.5555/3666122.3666235(2427-2462)Online publication date: 10-Dec-2023
https://dl.acm.org/doi/10.5555/3666122.3666235

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