Set-Cover Heuristics for Two-Level Logic Minimization

Abstract

Given a Boolean function, the Unate-Covering Problem (UCP) is NP-hard. This problem can be modeled as a setcover problem where minterms are the elements and implicants form the sets. Traditional solutions in logic synthesis use setcover algorithms that are oblivious to the special semantic of the elements and sets. We propose three new heuristics for the set-cover problem which are aware of the relationship between implicants and minterms. We show that the proposed heuristics are effective for breaking ties when a cyclic core is obtained. We evaluate the heuristics on a set of hard instances from BHOSLIB benchmark suite. We also replace ESPRESSO's set cover algorithm using these heuristics and compare the logic synthesis results. We further map the minimized Boolean equations using ABC's technology mapping tool using 2-input NAND gates and 4-input Lookup Tables (LUTs).

A Network-Based Deterministic Model for Causal Complexity

“…Several studies have proposed modifications to optimize the existing Quine-McCluskey algorithm (e.g. Jan et al [14]). The basis of these modifications were quite similar -to develop a modified method for generating prime implicants.…”

DenseQMC: an efficient bit-slice implementation of the Quine-McCluskey algorithm

“…However, a modern integer optimization suite may perform better (as noted already in [6]). In addition, there are several dedicated exact or approximate heuristic solvers for the SetCover problem in general [7,12,23], as well as methods tailored to the Boolean minimization problem [11].…”