Computing and estimating the volume of the solution space of SMT(LA) constraints

Ge, Cunjing; Ma, Feifei; Zhang, Peng; Zhang, Jian

doi:10.1016/j.tcs.2016.10.019

Cited by 10 publications

(10 citation statements)

References 27 publications

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“…The coefficients belong to [0, 10], the domain size is 64 and m = n, n ∈ {3, 4, 5}. • Simple Temporal Planning: We randomly generated 150 instances based on the structure of Simple Temporal Networks (STNs) [Huang et al, 2018]. • Instances from program analysis: We analyzed 7 programs ('cubature', 'gjk', 'http-parser', 'muFFT', 'Sim-pleXML', 'tcas' and 'timeout') ranging from 0.4k to 7.7k lines of source code via a symbolic execution bugfinding tool called CAnalyze [Xu et al, 2014] 3 and generated 3803 instances in total.…”

Section: Discussionmentioning

confidence: 99%

“…Recently, the hash-based approximate counters [Chakraborty et al, 2016b;Ge et al, 2018a] attract much attention for improving scalability and providing rigorous guarantees. For Satisfiability Modulo Theories (SMT) formulas, the counting problem is known as #SMT [Chistikov et al, 2015;Chakraborty et al, 2016a;Ge et al, 2018b], which is also an emerging topic in this realm.…”

Section: Introductionmentioning

confidence: 99%

“…The integer solution counting over LCs is also an important problem and has many applications, such as counting-based search [Zanarini and Pesant, 2007;Pesant, 2016], simple temporal planning [Huang et al, 2018] and probabilistic program analysis [Geldenhuys et al, 2012;Luckow et al, 2014]. This problem is proved to be #P-hard [Valiant, 1979].…”

Section: Introductionmentioning

confidence: 99%

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Approximating Integer Solution Counting via Space Quantification for Linear Constraints

et al. 2019

Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence

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Solution counting or solution space quantification (means volume computation and volume estimation) for linear constraints (LCs) has found interesting applications in various fields. Experimental data shows that integer solution counting is usually more expensive than quantifying volume of solution space while their output values are close. So it is helpful to approximate the number of integer solutions by the volume if the error is acceptable. In this paper, we present and prove a bound of such error for LCs. It is the first bound that can be used to approximate the integer solution counts. Based on this result, an approximate integer solution counting method for LCs is proposed. Experiments show that our approach is over 20x faster than the state-of-the-art integer solution counters. Moreover, such advantage increases with the problem scale.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Approximating Integer Solution Counting via Space Quantification for Linear Constraints

et al. 2019

Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence

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“…They found that the coordinate directions hitand-run method outperforms the commonly used hypersphere directions method with respect to not only runtime, but also accuracy. Besides, they proposed a re-utilization technique for sampling points which was proved no side-effect on the error [24]. A practical tool called PolyVest was implemented, which can efficiently handle general polytopes with dozens of dimensions.…”

Section: Volume Estimationmentioning

confidence: 99%

“…Therefore, by integrating volume estimation, exact integer counting and approximate integer counting methods introduced in Section 3 with DPLL(T) framework, one can estimate the volume of the solution space of SMT(LRA) formulas, and compute or approximate integer solution counts of SMT(LIA) formulas, respectively. [24] presented such an extension, and implemented a tool called VolCE for #SMT(LA) problems. Besides, they also introduced several strategies and preprocessing techniques on convex polytopes to improve the performance.…”

Section: #Smt(la)mentioning

confidence: 99%

Counting the Number of Solutions to Constraints

Zhang¹,

Ge²,

Ma³

2020

Preprint

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Compared with constraint satisfaction problems, counting problems have received less attention. In this paper, we survey research works on the problems of counting the number of solutions to constraints. The constraints may take various forms, including, formulas in the propositional logic, linear inequalities over the reals or integers, Boolean combination of linear constraints. We describe some techniques and tools for solving the counting problems, as well as some applications (e.g., applications to automated reasoning, program analysis, formal verification and information security).

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Monte-Carlo Integration on a Union of Polytopes

Stübbe,

Remke

2024

AIRO Springer Series

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Computing and estimating the volume of the solution space of SMT(LA) constraints

Cited by 10 publications

References 27 publications

Approximating Integer Solution Counting via Space Quantification for Linear Constraints

Approximating Integer Solution Counting via Space Quantification for Linear Constraints

Counting the Number of Solutions to Constraints

Monte-Carlo Integration on a Union of Polytopes

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