Approximate Counting in SMT and Value Estimation for Probabilistic Programs

Chistikov, Dmitry; Dimitrova, Rayna; Majumdar, Rupak

doi:10.1007/978-3-662-46681-0_26

Cited by 30 publications

(18 citation statements)

References 55 publications

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“…For completeness, ApproxMC [8,11] is listed here as Algorithm 1. Its inputs are a formula F and two accuracy parameters T and pivot.…”

Section: Preliminariesmentioning

confidence: 99%

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A New Probabilistic Algorithm for Approximate Model Counting

Tian

et al. 2018

Automated Reasoning

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Constrained counting is important in domains ranging from artificial intelligence to software analysis. There are already a few approaches for counting models over various types of constraints. Recently, hashing-based approaches achieve both theoretical guarantees and scalability, but still rely on solution enumeration. In this paper, a new probabilistic polynomial time approximate model counter is proposed, which is also a hashing-based universal framework, but with only satisfiability queries. A variant with a dynamic stopping criterion is also presented. Empirical evaluation over benchmarks on propositional logic formulas and SMT(BV) formulas shows that the approach is promising.

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“…For completeness, ApproxMC [8,11] is listed here as Algorithm 1. Its inputs are a formula F and two accuracy parameters T and pivot.…”

Section: Preliminariesmentioning

confidence: 99%

“…So Counting(F, p) invokes up to p times Solving(F) by this way. This method is adopted by all previous hashingbased ( , δ)-counters [8,11,6].…”

Section: Dynamic Stopping Criterionmentioning

confidence: 99%

A New Probabilistic Algorithm for Approximate Model Counting

Tian

et al. 2018

Automated Reasoning

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“…The approach is closely related to the mixture-of-polynomials density estimation for hybrid Bayesian networks [35]. Applications of WMI (and closely related formulations) for probabilistic graphical modeling and probabilistic programming tasks have also been emerging [14,1,29,7,12].…”

Section: Introductionmentioning

confidence: 99%

Scaling up Probabilistic Inference in Linear and Non-linear Hybrid Domains by Leveraging Knowledge Compilation

Fuxjaeger

Belle

2020

Proceedings of the 12th International Conference on Agents and Artificial Intelligence

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Weighted model integration (WMI) extends weighted model counting (WMC) in providing a computational abstraction for probabilistic inference in mixed discrete-continuous domains. WMC has emerged as an assembly language for state-of-the-art reasoning in Bayesian networks, factor graphs, probabilistic programs and probabilistic databases.In this regard, WMI shows immense promise to be much more widely applicable, especially as many real-world applications involve attribute and feature spaces that are continuous and mixed. Nonetheless, state-of-the-art tools for WMI are limited and less mature than their propositional counterparts.In this work, we propose a new implementation regime that leverages propositional knowledge compilation for scaling up inference. In particular, we use sentential decision diagrams, a tractable representation of Boolean functions, as the underlying model counting and model enumeration scheme. Our regime performs competitively to state-of-theart WMI systems, but is also shown, for the first time, to handle non-linear constraints over non-linear potentials.

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“…In our case the variables not counted need not be of bit-vector type. For instance this makes SearchMC to our knowledge the first tool that can be used to count models of constraints over floating-point numbers (counting the floating-point bit patterns individually, as contrasted with computing the measure of a subset of R n as in the work of Chistikov et al [13]). We demonstrate the use of this capability with an application to a security problem that arises in differential privacy mechanisms because of the limited precision of floating-point values.…”

Section: Introductionmentioning

confidence: 99%

Bit-Vector Model Counting Using Statistical Estimation

Kim

McCamant

2018

Tools and Algorithms for the Construction and Analysis of Systems

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Abstract. Approximate model counting for bit-vector SMT formulas (generalizing #SAT) has many applications such as probabilistic inference and quantitative information-flow security, but it is computationally difficult. Adding random parity constraints (XOR streamlining) and then checking satisfiability is an effective approximation technique, but it requires a prior hypothesis about the model count to produce useful results. We propose an approach inspired by statistical estimation to continually refine a probabilistic estimate of the model count for a formula, so that each XOR-streamlined query yields as much information as possible. We implement this approach, with an approximate probability model, as a wrapper around an off-the-shelf SMT solver or SAT solver. Experimental results show that the implementation is faster than the most similar previous approaches which used simpler refinement strategies. The technique also lets us model count formulas over floating-point constraints, which we demonstrate with an application to a vulnerability in differential privacy mechanisms.

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Approximate Counting in SMT and Value Estimation for Probabilistic Programs

Cited by 30 publications

References 55 publications

A New Probabilistic Algorithm for Approximate Model Counting

A New Probabilistic Algorithm for Approximate Model Counting

Scaling up Probabilistic Inference in Linear and Non-linear Hybrid Domains by Leveraging Knowledge Compilation

Bit-Vector Model Counting Using Statistical Estimation

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