Linear-Invariant Generation for Probabilistic Programs:

Katoen, Joost-Pieter; McIver, Annabelle; Meinicke, Larissa; Morgan, Carroll

doi:10.1007/978-3-642-15769-1_24

Cited by 81 publications

(104 citation statements)

References 17 publications

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“…PRINSYS [11] implements the constraint-based quantitative invariant synthesis approach developed by Katoen et al [14]. The tool uses a manually supplied template with unknown coefficients.…”

Section: Comparison With Prinsys[11]mentioning

confidence: 99%

“…We also compare our approach with the tool PRINSYS that synthesizes quantitative invariants using a constraint-based approach by solving constraints on the unknown coefficients of a template invariant form [13,11].…”

Section: Introductionmentioning

confidence: 99%

“…Furthermore, our technique synthesizes invariants that are polynomial expressions involving the program variables. In particular, indicator functions over program assertions are not considered in this paper [13,19]. Indicator functions complicate the computation of the preexpectation when a richer class of distributions are allowed.…”

Section: Introductionmentioning

confidence: 99%

“…The use of abstract interpretation framework is an additional contribution. The generation of quantitative invariants was first studied by Katoen et al [13], using a constraint-based approach [6,25], implemented in the tool PRINSYS [11]. An experimental comparison is provided in Section 5.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Expectation Invariants for Probabilistic Program Loops as Fixed Points

Chakarov

Sankaranarayanan

2014

Static Analysis

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We present static analyses for probabilistic loops using expectation invariants. Probabilistic loops are imperative while-loops augmented with calls to random value generators. Whereas, traditional program analysis uses Floyd-Hoare style invariants to over-approximate the set of reachable states, our approach synthesizes invariant inequalities involving the expected values of program expressions at the loop head. We first define the notion of expectation invariants, and demonstrate their usefulness in analyzing probabilistic program loops. Next, we present the set of expectation invariants for a loop as a fixed point of the pre-expectation operator over sets of program expressions. Finally, we use existing concepts from abstract interpretation theory to present an iterative analysis that synthesizes expectation invariants for probabilistic program loops. We show how the standard polyhedral abstract domain can be used to synthesize expectation invariants for probabilistic programs, and demonstrate the usefulness of our approach on some examples of probabilistic program loops.

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Section: Comparison With Prinsys[11]mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Expectation Invariants for Probabilistic Program Loops as Fixed Points

Chakarov

Sankaranarayanan

2014

Static Analysis

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“…Loops can be accommodated in two different ways: by assuming that the user provides loop invariants [35], or by assuming an outer (statistical) procedure that selects a finite set of executions that is sufficient for the analysis up to a given confidence level [51,52]. In either case, the core analysis problem reduces to analyzing finite-path unwindings of programs with loops, which is exactly what our model captures.…”

Section: Syntaxmentioning

confidence: 99%

Approximate counting in SMT and value estimation for probabilistic programs

2017

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#SMT, or model counting for logical theories, is a well-known hard problem that generalizes such tasks as counting the number of satisfying assignments to a Boolean formula and computing the volume of a polytope. In the realm of satisfiability modulo theories (SMT) there is a growing need for model counting solvers, coming from several application domains (quantitative information flow, static analysis of probabilistic programs). In this paper, we show a reduction from an approximate version of #SMT to SMT. We focus on the theories of integer arithmetic and linear real arithmetic. We propose model counting algorithms that provide approximate solutions with formal bounds on the approximation error. They run in polynomial time and make a polynomial number of queries to the SMT solver for the underlying theory, exploiting "for free" the sophisticated heuristics implemented within modern SMT solvers. We have implemented the algorithms and used them to solve the value problem for a model of loop-free probabilistic programs with nondeterminism.

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Ranking and Repulsing Supermartingales for Reachability in Probabilistic Programs

Takisaka

Oyabu

Urabe

et al. 2018

Lecture Notes in Computer Science

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Computing reachability probabilities is a fundamental problem in the analysis of probabilistic programs. This paper aims at a comprehensive and comparative account of various martingale-based methods for over-and underapproximating reachability probabilities. Based on the existing works that stretch across different communities (formal verification, control theory, etc.), we offer a unifying account. In particular, we emphasize the role of order-theoretic fixed points-a classic topic in computer science-in the analysis of probabilistic programs. This leads us to two new martingale-based techniques, too. We also make an experimental comparison using our implementation of template-based synthesis algorithms for those martingales.

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Linear-Invariant Generation for Probabilistic Programs:

Cited by 81 publications

References 17 publications

Expectation Invariants for Probabilistic Program Loops as Fixed Points

Expectation Invariants for Probabilistic Program Loops as Fixed Points

Approximate counting in SMT and value estimation for probabilistic programs

Ranking and Repulsing Supermartingales for Reachability in Probabilistic Programs

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