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Model-Counting Approaches for Nonlinear Numerical Constraints

  • Mateus BorgesEmail author
  • Quoc-Sang Phan
  • Antonio Filieri
  • Corina S. Păsăreanu
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10227)

Abstract

Model counting is of central importance in quantitative reasoning about systems. Examples include computing the probability that a system successfully accomplishes its task without errors, and measuring the number of bits leaked by a system to an adversary in Shannon entropy. Most previous work in those areas demonstrated their analysis on programs with linear constraints, in which cases model counting is polynomial time. Model counting for nonlinear constraints is notoriously hard, and thus programs with nonlinear constraints are not well-studied. This paper surveys state-of-the-art techniques and tools for model counting with respect to SMT constraints, modulo the bitvector theory, since this theory is decidable, and it can express nonlinear constraints that arise from the analysis of computer programs. We integrate these techniques within the Symbolic Pathfinder platform and evaluate them on difficult nonlinear constraints generated from the analysis of cryptographic functions.

Keywords

Model counting modulo theories Bitvector arithmetic Nonlinear constraints Cryptographic functions 

Notes

Acknowledgement

This work was funded in part by the National Science Foundation (NSF Grant Nos. CCF-1319858, CCF-1549161) and also by DARPA under agreement number FA8750-15-2-0087. The U.S. Government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright notation thereon. Mateus Borges is funded by an Imperial College PhD Scholarship.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Mateus Borges
    • 1
    Email author
  • Quoc-Sang Phan
    • 2
  • Antonio Filieri
    • 1
  • Corina S. Păsăreanu
    • 2
    • 3
  1. 1.Imperial College LondonLondonUK
  2. 2.Carnegie Mellon University Silicon ValleyMountain ViewUSA
  3. 3.NASA AmesMountain ViewUSA

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