Exact Toffoli Network Synthesis of Reversible Logic Using Boolean Satisfiability

Abstract

Compact synthesis result for reversible logic is of major interest in low-power design and quantum computing. Such reversible functions are realized as a cascade of Toffoli gates. In this paper, we present the first exact synthesis algorithm for reversible functions using generalized Toffoli gates. Our iterative algorithm formulates the synthesis problem with d Toffoli gates as a sequence of Boolean satisfiability (SAT) instances. Such an instance is satisfiable iff there exists a network representation with d gates. Thus we can guarantee minimality. For a set of benchmarks experimental results are given