Analysis of Bayesian Networks via Prob-Solvable Loops

Bartocci, Ezio; Kovács, Laura; Stankovič, Miroslav

doi:10.1007/978-3-030-64276-1_12

Cited by 20 publications

(16 citation statements)

References 32 publications

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“…The key to our approach is that the structural constraints of Prob-solvable loops allow for automatically computing almost sure asymptotic bounds on polynomials over program variables. Prob-solvable loops cover a vast set of complex and relevant probabilistic processes including random walks and dynamic Bayesian networks [5]. Only two out of 50 benchmarks in [10,42] are outside the scope of Prob-solvable loops regarding PAST certification.…”

Section: Resultsmentioning

confidence: 99%

“…AMBER and all bench-marks are available at https://github.com/probing-lab/amber. AMBER uses MORA [4] [6] for computing the first-order moments of program variables and the DIOFANT package 5 as its computer algebra system.…”

Section: Methodsmentioning

confidence: 99%

“…Let us illustrate this. Consider the following two input-output-pairs which our implementation would produce: (a) dominating({i 2 +10,10 5 is eventually greater than all functions in the input set modulo a constant factor because all functions in the input set are O(i 5 ). Therefore, i 5 dominates the input set.…”

Section: Methodsmentioning

confidence: 99%

“…However, many non-trivial probabilistic programs can be naturally modeled as succinct Prob-solvable loops. These include complex stochastic processes such as 2D random walks and dynamic Bayesian networks [5]. Almost all existing benchmarks on automated probabilistic termination analysis fall within the scope of Prob-solvable loops (cf.…”

Section: Remark 1 (Prob-solvable Expressiveness)mentioning

confidence: 99%

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Automated Termination Analysis of Polynomial Probabilistic Programs

Marcel

Bartocci

Katoen

et al. 2021

Programming Languages and Systems

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The termination behavior of probabilistic programs depends on the outcomes of random assignments. Almost sure termination (AST) is concerned with the question whether a program terminates with probability one on all possible inputs. Positive almost sure termination (PAST) focuses on termination in a finite expected number of steps. This paper presents a fully automated approach to the termination analysis of probabilistic while-programs whose guards and expressions are polynomial expressions. As proving (positive) AST is undecidable in general, existing proof rules typically provide sufficient conditions. These conditions mostly involve constraints on supermartingales. We consider four proof rules from the literature and extend these with generalizations of existing proof rules for (P)AST. We automate the resulting set of proof rules by effectively computing asymptotic bounds on polynomials over the program variables. These bounds are used to decide the sufficient conditions – including the constraints on supermartingales – of a proof rule. Our software tool Amber can thus check AST, PAST, as well as their negations for a large class of polynomial probabilistic programs, while carrying out the termination reasoning fully with polynomial witnesses. Experimental results show the merits of our generalized proof rules and demonstrate that Amber can handle probabilistic programs that are out of reach for other state-of-the-art tools.

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Section: Resultsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Remark 1 (Prob-solvable Expressiveness)mentioning

confidence: 99%

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Automated Termination Analysis of Polynomial Probabilistic Programs

Marcel

Bartocci

Katoen

et al. 2021

Programming Languages and Systems

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“…On a high-level, this constraint enables the use of algebraic recurrence techniques for probabilistic termination analysis [19]. Despite the syntactical restrictions, most existing benchmarks on automated probabilistic termination analysis [19] and dynamic Bayesian networks [3] can be encoded in our programming language. Figure 2 shows three example programs for which Amber is able to automatically infer the respective termination behavior.…”

Section: Usage and Componentsmentioning

confidence: 99%

The Probabilistic Termination Tool Amber

Marcel¹,

Bartocci²,

Katoen³

et al. 2021

Preprint

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We describe the Amber tool for proving and refuting the termination of a class of probabilistic while-programs with polynomial arithmetic, in a fully automated manner. Amber combines martingale theory with properties of asymptotic bounding functions and implements relaxed versions of existing probabilistic termination proof rules to prove/disprove (positive) almost sure termination of probabilistic loops. Amber supports programs parameterized by symbolic constants and drawing from common probability distributions. Our experimental comparisons give practical evidence of Amber outperforming existing state-of-the-art tools.

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