Solving Satisfiability Problems Using Reconfigurable Computing
Takayuki Suyama, Makoto Yokoo, Hiroshi Sawada, and Akira Nagoya
IEEE Transactions On Very Large Scale Integration (VLSI), (to appear)

This paper reports on an innovative approach for solving satisfiability problems for propositional formulas in conjunctive normal form (SAT) by creating a logic circuit that is specialized to solve each problem instance on Field Programmable Gate Arrays (FPGAs). This approach has become feasible due to recent advances in Reconfigurable Computing and has opened up an exciting new research field in algorithm design. SAT is an important subclass of constraint satisfaction problems, which can formalize a wide range of application problems.

We have developed a series of algorithms that are suitable for a logic circuit implementation, including an algorithm whose performance is equivalent to the Davis-Putnam procedure with powerful dynamic variable ordering. Simulation results show that this method can solve a hard random 3-SAT problem with 400 variables within 1.6 minutes at a clock rate of 10MHz. Faster speeds can be obtained by increasing the clock rate. Furthermore, we have actually implemented a 128-variable, 256-clause problem instance on FPGAs.