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Efficient Analysis of Probabilistic Programs with an Unbounded Counter

Authors:

Tomás Brázdil,

Stefan Kiefer,

Antonín KŭceraAuthors Info & Claims

Journal of the ACM (JACM), Volume 61, Issue 6

Article No.: 41, Pages 1 - 35

https://doi.org/10.1145/2629599

Published: 17 December 2014 Publication History

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Abstract

We show that a subclass of infinite-state probabilistic programs that can be modeled by probabilistic one-counter automata (pOC) admits an efficient quantitative analysis. We start by establishing a powerful link between pOC and martingale theory, which leads to fundamental observations about quantitative properties of runs in pOC. In particular, we provide a “divergence gap theorem”, which bounds a positive non-termination probability in pOC away from zero. Using these observations, we show that the expected termination time can be approximated up to an arbitrarily small relative error in polynomial time, and the same holds for the probability of all runs that satisfy a given ω-regular property encoded by a deterministic Rabin automaton.

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Finkel AHaddad SYe L(2023)Introducing Divergence for Infinite Probabilistic ModelsReachability Problems10.1007/978-3-031-45286-4_10(127-140)Online publication date: 5-Oct-2023
https://doi.org/10.1007/978-3-031-45286-4_10
Abdulla PAtig MAgarwal RGodbole AS. K(2022)Probabilistic Total Store OrderingProgramming Languages and Systems10.1007/978-3-030-99336-8_12(317-345)Online publication date: 29-Mar-2022
https://doi.org/10.1007/978-3-030-99336-8_12
Brázdil TChatterjee KKučera ANovotný PVelan D(2019)Deciding Fast Termination for Probabilistic VASS with NondeterminismAutomated Technology for Verification and Analysis10.1007/978-3-030-31784-3_27(462-478)Online publication date: 28-Oct-2019
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Index Terms

Efficient Analysis of Probabilistic Programs with an Unbounded Counter
1. Theory of computation
  1. Semantics and reasoning
    1. Program reasoning
      1. Program verification

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Reviews

Reviewer: Kamal Lodaya

The authors consider a probabilistic recursive program working on data of unbounded size, for example, with a geometric probability distribution for what the data looks like. This makes sense for common data structures like trees. Is the expected time that the program will terminate finite__?__ Is it almost sure (probability 1) that all runs, finite and infinite, satisfy a property specified by a deterministic Rabin automaton on infinite words__?__ When the program can be modeled as a probabilistic one-counter automaton, the authors show such questions can be answered in polynomial time. An earlier work considered more general probabilistic pushdown systems, but used the decidability of the existential theory of the reals, which has greater complexity. The main idea is that although the system is modeled as an infinite Markov chain, the questions can be answered by analyzing another finite Markov chain with some "good" conditions. The paper is quite technical; the justification that these ideas are correct involves the construction of suitable martingales. Online Computing Reviews Service

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Published In

Journal of the ACM Volume 61, Issue 6

November 2014

285 pages

ISSN:0004-5411

EISSN:1557-735X

DOI:10.1145/2700084

Editor:
Victor Vianu
University of California, San Diego

Issue’s Table of Contents

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Association for Computing Machinery

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Publication History

Published: 17 December 2014

Accepted: 01 April 2014

Revised: 01 September 2013

Received: 01 April 2012

Published in JACM Volume 61, Issue 6

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Finkel AHaddad SYe L(2023)Introducing Divergence for Infinite Probabilistic ModelsReachability Problems10.1007/978-3-031-45286-4_10(127-140)Online publication date: 5-Oct-2023
Abdulla PAtig MAgarwal RGodbole AS. K(2022)Probabilistic Total Store OrderingProgramming Languages and Systems10.1007/978-3-030-99336-8_12(317-345)Online publication date: 29-Mar-2022
Brázdil TChatterjee KKučera ANovotný PVelan D(2019)Deciding Fast Termination for Probabilistic VASS with NondeterminismAutomated Technology for Verification and Analysis10.1007/978-3-030-31784-3_27(462-478)Online publication date: 28-Oct-2019
Wang DHoffmann JReps T(2018)PMAF: an algebraic framework for static analysis of probabilistic programsACM SIGPLAN Notices10.1145/3296979.319240853:4(513-528)Online publication date: 11-Jun-2018
Wang DHoffmann JReps TFoster JGrossman D(2018)PMAF: an algebraic framework for static analysis of probabilistic programsProceedings of the 39th ACM SIGPLAN Conference on Programming Language Design and Implementation10.1145/3192366.3192408(513-528)Online publication date: 11-Jun-2018
Mayr RSchewe STotzke PWojtczak DAceto LIngólfsdóttir A(2017)MDPs with energy-parity objectivesProceedings of the 32nd Annual ACM/IEEE Symposium on Logic in Computer Science10.5555/3329995.3330066(1-12)Online publication date: 20-Jun-2017
Chatterjee KNovotný PŽikelić Ð(2017)Stochastic invariants for probabilistic terminationACM SIGPLAN Notices10.1145/3093333.300987352:1(145-160)Online publication date: 1-Jan-2017
Chatterjee KNovotný PŽikelić ÐCastagna GGordon A(2017)Stochastic invariants for probabilistic terminationProceedings of the 44th ACM SIGPLAN Symposium on Principles of Programming Languages10.1145/3009837.3009873(145-160)Online publication date: 1-Jan-2017
Mayr RSchewe STotzke PWojtczak D(2017)MDPs with energy-parity objectives2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)10.1109/LICS.2017.8005131(1-12)Online publication date: Jun-2017
Castagna GGordon A(2017)Proceedings of the 44th ACM SIGPLAN Symposium on Principles of Programming LanguagesundefinedOnline publication date: 1-Jan-2017
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Zero-reachability in probabilistic multi-counter automata

The complexity of regular abstractions of one-counter languages

Pushdown and One-Counter Automata: Constant and Non-constant Memory Usage

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Recommendations

Zero-reachability in probabilistic multi-counter automata

The complexity of regular abstractions of one-counter languages

Pushdown and One-Counter Automata: Constant and Non-constant Memory Usage

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