Efficient BDDs for bounded arithmetic constraints

Authors:
Constantinos Bartzis;Tevfik Bultan
Affiliations:
Department of Computer Science, University of California, 93106, Santa Barbara, CA, USA;Department of Computer Science, University of California, 93106, Santa Barbara, CA, USA
Venue:
International Journal on Software Tools for Technology Transfer (STTT) - Special section on Tools and Algorithms for the Construction and Analysis of Systems
Year:
2006

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Abstract

Symbolic model checkers use BDDs to represent arithmetic constraints over bounded integer variables. The size of such BDDs can in the worst case be exponential in the number and size (in bits) of the integer variables. In this paper we show how to construct linear-sized BDDs for linear integer arithmetic constraints. We present basic constructions for atomic equality and inequality constraints and generalize our complexity results for arbitrary linear arithmetic formulas. We also present three alternative ways of handling out-of-bounds transitions and discuss heterogeneous bounds on integer variables. We experimentally compare our approach to other BDD-based symbolic model checkers and demonstrate that the algorithms presented in this paper can be used to improve their performance significantly.