CAV 1997: Computer Aided Verification pp 60-71

# An efficient decision procedure for the theory of fixed-sized bit-vectors

• David Cyrluk
• Oliver Möller
• Harald Rueß
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1254)

## Abstract

In this paper we describe a decision procedure for the core theory of fixed-sized bit-vectors with extraction and composition that can readily be integrated into Shostak's procedure for deciding combinations of theories. Inputs to the solver are unquantified bit-vector equations t=u and the algorithm returns true if t=u is valid in the bit-vector theory, false if t=u is unsatisfiable, and a system of solved equations otherwise. The time complexity of the solver is $$\mathcal{O}\left( {\left| t \right| \cdot log{\text{ }}n + n^2 } \right)$$, where t is the length of the bit-vector term t and n denotes the number of bits on either side of the equation. Then, the solver for the core bit-vector theory is extended to handle other bit-vector operations like bitwise logical operations, shifting, and arithmetic interpretations of bit-vectors. We develop a BDD-like data-structure called bit-vector BDDs to represent bit-vectors, various operations on bit-vectors, and a solver on bit-vector BDDs.

## Keywords

Decision Procedure Simple Term Core Theory Core Solver Bitwise Operation
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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## Authors and Affiliations

• David Cyrluk
• 1
• Oliver Möller
• 2
• Harald Rueß
• 2
1. 1.Computer Science LaboratorySRI InternationalMenlo ParkUSA
2. 2.Fakultät für InformatikUniversität UlmUlmGermany