Efficient computation of canonical form for Boolean matching in large libraries

Abstract

This paper presents an efficient technique for solving a Boolean matching problem in cell-library binding, where the number of cells in the library is large. As a basis of the Boolean matching, we use the notion NP-representative (NPR); two functions have the same NPR if one can be obtained from the other by a permutation and/or complementation(s) of the variables. By using a table look-up and a tree-based breadth-first search strategy, our method quickly computes NPR for a given function. Boolean matching of the given function against the whole library is determined by checking the presence of its NPR in a hash table, which stores NPRs for all the library functions and their complements. The effectiveness of our method is demonstrated through experimental results, which shows that it is more than two orders of magnitude faster than the Hinsberger-Kolla's algorithm---the fastest Boolean matching algorithm for large libraries.