Chistikov, D., Dimitrova, R. and Majumdar, R. (2015) Approximate counting in SMT and value estimation for probabilistic programs. In: Baier, C. and Tinelli, C., (eds.) Tools and Algorithms for the Construction and Analysis of Systems - 21st International Conference, TACAS 2015. Tools and Algorithms for the Construction and Analysis of Systems, 11-18 Apr 2015, London, UK. Lecture Notes in Computer Science (9035). Springer , pp. 320-334. ISBN 9783662466803
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 a value estimation problem for a model of loop-free probabilistic programs with nondeterminism.
Metadata
Item Type: | Proceedings Paper |
---|---|
Authors/Creators: |
|
Editors: |
|
Copyright, Publisher and Additional Information: | © 2015 Springer-Verlag. This is an author-produced version of a paper subsequently published in TACAS 2015. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Hash Function; Boolean Formula; Probabilistic Program; Satisfying Assignment; Integer Arithmetic |
Dates: |
|
Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Computer Science (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 04 Feb 2020 14:22 |
Last Modified: | 05 Feb 2020 15:47 |
Status: | Published |
Publisher: | Springer |
Series Name: | Lecture Notes in Computer Science |
Refereed: | Yes |
Identification Number: | 10.1007/978-3-662-46681-0_26 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:156434 |