Computer Science Department
School of Computer Science, Carnegie Mellon University


Using SAT based Image Computation
for Reachability Analysis

Pankaj Chauhan, Edmund M. Clarke, Daniel Kroening

September 2003

Keywords: Hardware verification, SAT

Satisfiability procedures have shown significant promise for symbolic simulation of large circuits, hence they have been used in many formal verification techniques, including automated abstraction refinement, ATPG etc. We show how to use modern SAT solvers like Chaff and GRASP to compute images of sets of states and how to efficiently detect fixed point of the sets of states during reachability analysis. Our method is completely SAT based, and does not use BDDs at all. The sets of states and transition relation are represented in clausal form, which can be processed by SAT checkers. The SAT checker subsequently generates the set of newly reached states in clausal form as well. At the heart of our engine lie two efficient algorithms. The first algorithm shortens the cubes that the SAT checker generates by a static-analysis algorithm, which significantly reduces the number of cubes the SAT checker needs to enumerate. The second algorithm reduces the space required to store sets of states as a set of cubes by a recursive cube-merging procedure. We demonstrate the effectiveness of our procedure on ISCAS sequential benchmarks for reachability. In particular, our algorithm does not have BDD size explosion surprises and deteriorates in a predictable manner.

18 pages

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