Chapter

Tools and Algorithms for the Construction and Analysis of Systems

Volume 4424 of the series Lecture Notes in Computer Science pp 358-372

Deciding Bit-Vector Arithmetic with Abstraction

  • Randal E. BryantAffiliated withCarnegie Mellon University, Pittsburgh
  • , Daniel KroeningAffiliated withETH Zürich
  • , Joël OuaknineAffiliated withOxford University Computing Laboratory
  • , Sanjit A. SeshiaAffiliated withUniversity of California, Berkeley
  • , Ofer StrichmanAffiliated withThe Technion, Haifa
  • , Bryan BradyAffiliated withUniversity of California, Berkeley

Abstract

We present a new decision procedure for finite-precision bit-vector arithmetic with arbitrary bit-vector operations. Our procedure alternates between generating under- and over-approximations of the original bit-vector formula. An under-approximation is obtained by a translation to propositional logic in which some bit-vector variables are encoded with fewer Boolean variables than their width. If the under-approximation is unsatisfiable, we use the unsatisfiable core to derive an over-approximation based on the subset of predicates that participated in the proof of unsatisfiability. If this over-approximation is satisfiable, the satisfying assignment guides the refinement of the previous under-approximation by increasing, for some bit-vector variables, the number of Boolean variables that encode them. We present experimental results that suggest that this abstraction-based approach can be considerably more efficient than directly invoking the SAT solver on the original formula as well as other competing decision procedures.