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Volume Computation for Boolean Combination of Linear Arithmetic Constraints

  • Conference paper
Automated Deduction – CADE-22 (CADE 2009)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 5663))

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Abstract

There are many works on the satisfiability problem for various logics and constraint languages, such as SAT and Satisfiability Modulo Theories (SMT). On the other hand, the counting version of decision problems is also quite important in automated reasoning. In this paper, we study a counting version of SMT, i.e., how to compute the volume of the solution space, given a set of Boolean combinations of linear constraints. The problem generalizes the model counting problem and the volume computation problem for convex polytopes. It has potential applications to program analysis and verification, as well as approximate reasoning, yet it has received little attention. We first give a straightforward method, and then propose an improved algorithm. We also describe two ways of incorporating theory-level lemma learning technique into the algorithm. They have been implemented, and some experimental results are given. Through an example program, we show that our tool can be used to compute how often a given program path is executed.

This work is supported by the National Science Foundation of China (NSFC) under grant No. 60673044. Correspondence to: Jian Zhang, P.O.Box 8718, Beijing 100190, CHINA.

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Authors and Affiliations

  1. State Key Laboratory of Computer Science Institute of Software, Chinese Academy of Sciences, China

    Feifei Ma, Sheng Liu & Jian Zhang

  2. Graduate University, Chinese Academy of Sciences, China

    Feifei Ma & Sheng Liu

Authors
  1. Feifei Ma
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  2. Sheng Liu
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  3. Jian Zhang
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Editors and Affiliations

  1. School of Computer Science, The University of Manchester, Manchester, UK

    Renate A. Schmidt

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Ma, F., Liu, S., Zhang, J. (2009). Volume Computation for Boolean Combination of Linear Arithmetic Constraints. In: Schmidt, R.A. (eds) Automated Deduction – CADE-22. CADE 2009. Lecture Notes in Computer Science(), vol 5663. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02959-2_33

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  • DOI: https://doi.org/10.1007/978-3-642-02959-2_33

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02958-5

  • Online ISBN: 978-3-642-02959-2

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