Symmetry detection for large Boolean functions using circuit representation, simulation, and satisfiability

Abstract

Classical two-variable symmetries play an important role in many EDA applications, ranging from logic synthesis to formal verification. This paper proposes a complete circuit-based method that makes uses of structural analysis, integrated simulation and Boolean satisfiability for fast and scalable detection of classical symmetries of completely-specified Boolean functions. This is in contrast to previous incomplete circuit-based methods and complete BDD-based methods. Experimental results demonstrate that the proposed method works for large Boolean functions, for which BDDs cannot be constructed.

A Semi-Canonical Form for Sequential AIGs

“…Related previous work includes methods for symmetry detection, focused on computing automorphisms of digital circuits [5][6] [9][13] [18] and functional symmetries [16] [19] with applications in BDD variable reordering [17], reachability analysis [8], logic synthesis [15], SAT [1] [12], and post-placement rewiring [7], to mention just a few.…”

An Anytime Algorithm for Generalized Symmetry Detection in ROBDDs

“…This algorithm is underpinned by new symmetry relationships which take the form, that if T xi,xj p (f ) and T xj,x k q (f ) hold then T xi,xj r (f ) holds where T p , T q and T r denote one of the 12 generalized symmetry types. Only a few of these transitivity results have been previously reported [22] and these results could well find application in other symmetry detection problems [23].…”

“…An interesting thread of related research focusses on the problem of extracting symmetries from Boolean functions that are not represented as ROBDDs [23], [28].…”

Improvements to combinational equivalence checking

“…For example, it can be used to compute node flexibilities, such as don't-cares and resubstitutions [28], or canonical function properties, such as classical symmetries [42].…”