Automated Termination Analysis of Polynomial Probabilistic Programs

Marcel, Moosbrugger,; Bartocci, Ezio; Katoen, Joost-Pieter; Kovács, Laura

doi:10.26226/morressier.604907f41a80aac83ca25d19

Cited by 4 publications

(3 citation statements)

References 39 publications

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“…Various martingale-based approaches, such as [15,19,20,2,43], aim to synthesize probabilistic loop invariants over R-valued variables, see [49] for a recent survey. Most of these approaches yield invariants for proving almost-sure termination or bounding expected runtimes, [1] employs a CEGIS loop to train a neural network for learning a ranking supermartingale proving positive almost-sure termination of (possibly continuous) probabilistic programs.…”

Section: Related Workmentioning

confidence: 99%

Probabilistic Program Verification via Inductive Synthesis of Inductive Invariants

Batz¹,

Chen²,

Junges³

et al. 2022

Preprint

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A desired property of randomized systems, represented by probabilistic programs, is that the probability to reach some error state is sufficiently small; verification of such properties is often addressed by probabilistic model checking. We contribute an inductive synthesis approach for proving quantitative reachability properties by finding inductive invariants on source-code level. Our prototype implementation of various flavors of this approach shows promise: it finds inductive invariants for (in)finite-state programs, while beating state-of-the-art model checkers on some benchmarks and often outperforming monolithic alternatives.

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Section: Related Workmentioning

confidence: 99%

Probabilistic Program Verification via Inductive Synthesis of Inductive Invariants

Batz¹,

Chen²,

Junges³

et al. 2022

Preprint

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“…Experimental Setup. All our seven examples in Table 1 implement polynomial loop updates and fall in the class of probabilistic loops supported by [30].…”

Section: Experimental Evaluationmentioning

confidence: 99%

“…As such, for each example of Table 1, exact higher-order moments of random loop variables can be computed using the algorithmic approach of [30]. In our work, we use the Polar tool of [30] to derive a finite set M of exact higher-order moments for each PP of Table 1, and we set S M = M to be further used in Algorithm 1. Further, we generate our sampled data (Sample Data ) by executing each PP e = 1000 times and for loop iteration n = 100.…”

Section: Experimental Evaluationmentioning

confidence: 99%

Distribution Estimation for Probabilistic Loops

Karimi¹,

Marcel²,

Stankovič³

et al. 2022

Preprint

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We present an algorithmic approach to estimate the value distributions of random variables of probabilistic loops whose statistical moments are (partially) known. Based on these moments, we apply two statistical methods, Maximum Entropy and Gram-Charlier series, to estimate the distributions of the loop's random variables. We measure the accuracy of our distribution estimation by comparing the resulting distributions using exact and estimated moments of the probabilistic loop, and performing statistical tests. We evaluate our method on several probabilistic loops with polynomial updates over random variables drawing from common probability distributions, including examples implementing financial and biological models. For this, we leverage symbolic approaches to compute exact higher-order moments of loops as well as use sampling-based techniques to estimate moments from loop executions. Our experimental results provide practical evidence of the accuracy of our method for estimating distributions of probabilistic loop outputs.

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