Symmetry Detection and Boolean Matching Utilizing a Signature-Based Canonical Form of Boolean Functions

A Transform-Parametric Approach to Boolean Matching

“…More recent developments have led to canonical forms for P-equivalence as well [1], [7], [11]. In this paper, we compare our approach to the most performant of these previous works [1].…”

“…[6] improves the approach by pruning the search tree, using signatures (including first order cofactors) and symmetry checks. These approaches are slower than canonical form based methods [1], except for very small numbers of input variables, but their main drawback is the large memory requirements, which effectively limit its applicability to functions with up to a maximum of dozen variables [6], [9]. Canonical form-based approaches, on the other hand, scales well up to over twenty input variables.…”

“…complexity, where n is the number of input variables. An efficient algorithm to find the lexicographical maximum of a given function is presented in [1]. This algorithm still has to face the issue of dealing with functions that have a codomain of small cardinality ({0, 1}), and therefore cause frequent collisions when trying to discriminate variables.…”

“…In this paper, we propose a novel approach that tries to unify some of the most effective Boolean matching approaches based on canonical forms, ranging from those based on spectral function analysis [10], defined and developed in the '70s, to the most recent, based on functions representation by means of cofactors [1].…”

“…For an accurate and fair comparison, we reimplemented the most performant previous approach [1], and performed tests on both random function sets and specific functions that are considered worst cases.…”