Volume Computation for Boolean Combination of Linear Arithmetic Constraints

  • Feifei Ma
  • Sheng Liu
  • Jian Zhang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5663)


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.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Feifei Ma
    • 1
    • 2
  • Sheng Liu
    • 1
    • 2
  • Jian Zhang
    • 1
  1. 1.State Key Laboratory of Computer Science Institute of SoftwareChinese Academy of SciencesChina
  2. 2.Graduate University, Chinese Academy of SciencesChina

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