Approximate counting in SMT and value estimation for probabilistic programs

#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...

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Bibliographic Details
Published in:Acta informatica Vol. 54; no. 8; pp. 729 - 764
Main Authors: Chistikov, Dmitry, Dimitrova, Rayna, Majumdar, Rupak
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.12.2017
Springer Nature B.V
Subjects:
Algorithms
Arithmetic
Boolean algebra
Computer programming
Computer Science
Computer Systems Organization and Communication Networks
Data Structures and Information Theory
Information flow
Information Systems and Communication Service
Integer programming
Logics and Meanings of Programs
Original Article
Polynomials
Software Engineering/Programming and Operating Systems
Solvers
Static code analysis
Theory of Computation
ISSN:0001-5903, 1432-0525
Online Access:Get full text
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Summary:#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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ISSN:0001-5903
1432-0525
DOI:10.1007/s00236-017-0297-2