A new proof rule for almost-sure termination

We consider the problem of expected cost analysis over nondeterministic probabilistic programs, which aims at automated methods for analyzing the resource-usage of such programs. Previous approaches for this problem could only handle nonnegative bounded costs. However, in many scenarios, such as queuing networks or analysis of cryptocurrency protocols, both positive and negative costs are necessary and the costs are unbounded as well.In this work, we present a sound and efficient approach to obtain polynomial bounds on the expected accumulated cost of nondeterministic probabilistic programs. Our approach can handle (a) general positive and negative costs with bounded updates in variables; and (b) nonnegative costs with general updates to variables. We show that several natural examples which could not be handled by previous approaches are captured in our framework.Moreover, our approach leads to an efficient polynomialtime algorithm, while no previous approach for cost analysis of probabilistic programs could guarantee polynomial runtime. Finally, we show the effectiveness of our approach using experimental results on a variety of programs for which we efficiently synthesize tight resource-usage bounds.

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“…Termination analysis of probabilistic programs is a widelystudied topic. For automated approaches, see [1,16,18,71].…”

Section: Runs and Schedulersmentioning

confidence: 99%

Cost analysis of nondeterministic probabilistic programs

Wang

Goharshady

et al. 2019

Proceedings of the 40th ACM SIGPLAN Conference on Programming Language Design and Implementation

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“…Almost-sure termination is the classical and most widely-studied problem that extends termination of non-probabilistic programs, and is considered as a core problem in the programming languages community. See [Agrawal et al 2018;Chatterjee et al 2016bChatterjee et al , 2017Fioriti and Hermanns 2015;McIver et al 2018]. Proving finite termination of a program is much more ideal and probably the first goal of an analyzer.…”

Section: Introductionmentioning

confidence: 99%

Modular verification for almost-sure termination of probabilistic programs

Huang

Chatterjee

et al. 2019

Proc. ACM Program. Lang.

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In this work, we consider the almost-sure termination problem for probabilistic programs that asks whether a given probabilistic program terminates with probability 1. Scalable approaches for program analysis often rely on modularity as their theoretical basis. In non-probabilistic programs, the classical variant rule (V-rule) of Floyd-Hoare logic provides the foundation for modular analysis. Extension of this rule to almost-sure termination of probabilistic programs is quite tricky, and a probabilistic variant was proposed in [Fioriti and Hermanns 2015]. While the proposed probabilistic variant cautiously addresses the key issue of integrability, we show that the proposed modular rule is still not sound for almost-sure termination of probabilistic programs.Besides establishing unsoundness of the previous rule, our contributions are as follows: First, we present a sound modular rule for almost-sure termination of probabilistic programs. Our approach is based on a novel notion of descent supermartingales. Second, for algorithmic approaches, we consider descent supermartingales that are linear and show that they can be synthesized in polynomial time. Finally, we present experimental results on a variety of benchmarks and several natural examples that model various types of nested while loops in probabilistic programs and demonstrate that our approach is able to efficiently prove their almost-sure termination property.

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“…Alternatively, Thm. 18 could also be proved by combining several recent results on probabilistic programs: The approach of [28] could be used to show that µ P = 0 implies AST. Moreover, one could prove that µ P < 0 implies PAST by showing that x is a ranking supermartingale of the program [5,11,14,18].…”

Section: Deciding Terminationmentioning

confidence: 97%

“…Related Work. Many techniques to analyze (P)AST have been developed, which mostly rely on ranking supermartingales, e.g., [1,5,11,13,14,18,20,28,30]. Indeed, several of these works (e.g., [1,5,18,20]) present complete criteria for (P)AST, although (P)AST is undecidable.…”

Section: Conclusion Implementation and Related Workmentioning

confidence: 99%

Computing Expected Runtimes for Constant Probability Programs

Giesl

Hark

2019

Lecture Notes in Computer Science

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We introduce the class of constant probability (CP) programs and show that classical results from probability theory directly yield a simple decision procedure for (positive) almost sure termination of programs in this class. Moreover, asymptotically tight bounds on their expected runtime can always be computed easily. Based on this, we present an algorithm to infer the exact expected runtime of any CP program.

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A new proof rule for almost-sure termination

Cited by 73 publications

References 23 publications

Cost analysis of nondeterministic probabilistic programs

Cost analysis of nondeterministic probabilistic programs

Modular verification for almost-sure termination of probabilistic programs

Computing Expected Runtimes for Constant Probability Programs

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