Synthesizing Shortest Linear Straight-Line Programs over GF(2) Using SAT

  • Carsten Fuhs
  • Peter Schneider-Kamp
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6175)

Abstract

Non-trivial linear straight-line programs over the Galois field of two elements occur frequently in applications such as encryption or high-performance computing. Finding the shortest linear straight-line program for a given set of linear forms is known to be MaxSNP-complete, i.e., there is no ε-approximation for the problem unless P = NP.

This paper presents a non-approximative approach for finding the shortest linear straight-line program. In other words, we show how to search for a circuit of XOR gates with the minimal number of such gates. The approach is based on a reduction of the associated decision problem (“Is there a program of length k?”) to satisfiability of propositional logic. Using modern SAT solvers, optimal solutions to interesting problem instances can be obtained.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Carsten Fuhs
    • 1
  • Peter Schneider-Kamp
    • 2
  1. 1.LuFG Informatik 2RWTH Aachen UniversityGermany
  2. 2.IMADAUniversity of Southern DenmarkDenmark

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