Hypergraph isomorphism and structural equivalence of Boolean functions

Abstract

We show that hypergraph isomorphism can be tested in time O(cn), where n is the size of the vertex set. In general, input of a hypergraph could require Ω(2n) space, in which case the isomorphism test is in polynomial time. As a consequence, we put into polynomial time the classic problem of testing whether two Boolean functions, given by truth tables, are related via permutations and complementations of the variables, and therefore have structurally identical network realizations. In fact, the method is parallelizable and we put the problem even into NC. We obtain similarly an NC test of equivalence of truth tables under permutation of variables alone.