Boolean matching using generalized Reed-Muller forms

Abstract

--In this paper we present a new method for Boolean matching of completely specified Boolean functions. The canonical Generalized Reed-Muller forms are used as a powerful analysis tool. Input permutation, as well as input and output negation for matching are handled simultaneously. To reduce the search space for input correspondence, we have developed a method that can detect symmetries of any number of inputs simultaneously. Experiments on MCNC benchmark circuits are very encouraging.

Linear cofactor relationships in Boolean functions

“…Classical symmetries have been used as signatures for Boolean matching [5], [6], [27], [28]. We will show that using LCRs as signatures increase the distinguishing power significantly, compared to that of classical symmetries.…”

“…With the efficient computation algorithm proposed in this paper, LCRs can easily be incorporated as filters to quickly prune unnecessary tautology checks. Other techniques [5], [6], [27], [28] can also be used in combination with LCRs to facilitate the task of Boolean matching.…”

A universal symmetry detection algorithm

“…Anti-symmetry (Tsai and Marek-Sadowska 1994) (which is also known as Skew Symmetry and Negative Symmetry) was initially defined in terms of symmetric variable pairs. As with other symmetries, the anti-symmetries are defined with respect to the four cofactors f 00 , f 01 , f 10 and f 11 , taken with respect to the variables x i and x j .…”

Using decision diagrams to design ULMs for FPGAs

“…For recognizing the order and polarity of inputs and outputs of each block, we have implemented an algorithm based on Generalized Reed-Muller form matching, as in [25].…”