Fast Boolean matching with don't cares

This paper describes a fast Boolean matching algorithm which checks the containment relationship between an incompletely specified function and a completely specified function under permutation and negation on the input variables. The algorithm is designed for the pattern matching problem in technology mapping. It exploits functional symmetries of patterns and utilizes a compact data structure: binary permutation matrix. Using this matrix, nonmatching permutations and phase assignments can be pruned efficiently. All legal permutations and phase assignments, leading to a matching, can be obtained, as well. The experimental results on the MCNC benchmarks show that, compared with other Boolean matching approaches, our algorithm is at least 1,500 times faster for a common pattern abed + efgh and 58,000 times faster for another common pattern ab + cd + ef + gh. The matching speed for completely specified functions is also comparable to state-of-the-art matching algorithms