Solution of systems of Boolean equations via the integer domain

Authors:
Ahmed H. Abdel-Gawad;Amir F. Atiya;Nevin M. Darwish
Affiliations:
Department of Computer Engineering, Cairo University, Giza, Egypt;Department of Computer Engineering, Cairo University, Giza, Egypt;Department of Computer Engineering, Cairo University, Giza, Egypt
Venue:
Information Sciences: an International Journal
Year:
2010

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Abstract

This paper presents a new method for solving systems of Boolean equations. The method is based on converting the equations so that we operate in the integer domain. In the integer domain better and more efficient methodologies for solving equations are available. The conversion leads us to a system of polynomial equations obeying certain characteristics. A method is proposed for solving these equations. The most computationally demanding step is the repeated multiplication of polynomials. We develop a method for this problem that is significantly faster than the standard approach. We also introduce another variant of the method, the so-called hybrid approach, that leads to reduced memory requirements. Theoretical and experimental results indicate the superior performance of the proposed method and its variant compared to the competing methods. The proposed method is also validated by applying it to the problem of hardware verification.