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Approximate counting in SMT and value estimation for probabilistic programs
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Chistikov, Dmitry, Dimitrova, Rayna and Majumdar, Rupak (2017) Approximate counting in SMT and value estimation for probabilistic programs. ACTA Informatica, 54 (8). pp. 729-764. doi:10.1007/s00236-017-0297-2 ISSN 0001-5903.
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Official URL: http://dx.doi.org/10.1007/s00236-017-0297-2
Abstract
#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.
| Item Type: | Journal Article | ||||||||
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| Subjects: | Q Science > QA Mathematics > QA75 (Please use QA76 Electronic Computers. Computer Science) | ||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Computer Science | ||||||||
| Library of Congress Subject Headings (LCSH): | Constraint programming (Computer science), Logic, Symbolic and mathematical, Statistical decision, Algebra, Boolean | ||||||||
| Journal or Publication Title: | ACTA Informatica | ||||||||
| Publisher: | Springer | ||||||||
| ISSN: | 0001-5903 | ||||||||
| Official Date: | December 2017 | ||||||||
| Dates: |
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| Volume: | 54 | ||||||||
| Number: | 8 | ||||||||
| Page Range: | pp. 729-764 | ||||||||
| DOI: | 10.1007/s00236-017-0297-2 | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | Published | ||||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||||
| Date of first compliant deposit: | 19 June 2017 | ||||||||
| Date of first compliant Open Access: | 12 April 2018 |
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