A Method for Symbolic Computation of Abstract Operations

  • Aditya Thakur
  • Thomas Reps
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7358)


This paper helps to bridge the gap between (i) the use of logic for specifying program semantics and performing program analysis, and (ii) abstract interpretation. Many operations needed by an abstract interpreter can be reduced to the problem of symbolic abstraction: the symbolic abstraction of a formula ϕ in logic Open image in new window , denoted by Open image in new window , is the most-precise value in abstract domain Open image in new window that over-approximates the meaning of ϕ. We present a parametric framework that, given Open image in new window and Open image in new window , implements Open image in new window . The algorithm computes successively better over-approximations of Open image in new window . Because it approaches Open image in new window from “above”, if it is taking too much time, a safe answer can be returned at any stage.

Moreover, the framework is“dual-use”: in addition to its applications in abstract interpretation, it provides a new way for an SMT (Satisfiability Modulo Theories) solver to perform unsatisfiability checking: given Open image in new window , the condition Open image in new window implies that ϕ is unsatisfiable.


Basic Block Symbolic Computation Integrity Constraint Abstract Interpretation Satisfiability Modulo Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Aditya Thakur
    • 1
  • Thomas Reps
    • 1
    • 2
  1. 1.Computer Sciences DepartmentUniversity of WisconsinMadisonUSA
  2. 2.GrammaTech, Inc.IthacaUSA

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