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

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Theory and Applications of Satisfiability Testing – SAT 2010 (SAT 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,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.

Supported by the G.I.F. grant 966-116.6 and the Danish Natural Science Research Council.

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Author information

Authors and Affiliations

  1. LuFG Informatik 2, RWTH Aachen University, Germany

    Carsten Fuhs

  2. IMADA, University of Southern Denmark, Denmark

    Peter Schneider-Kamp

Authors
  1. Carsten Fuhs
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  2. Peter Schneider-Kamp
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Editor information

Editors and Affiliations

  1. Technion, Technion City, 32000, Haifa, Israel

    Ofer Strichman

  2. Vienna University of Technology, Favoritenstr. 9-11, 1040, Vienna, Austria

    Stefan Szeider

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Fuhs, C., Schneider-Kamp, P. (2010). Synthesizing Shortest Linear Straight-Line Programs over GF(2) Using SAT. In: Strichman, O., Szeider, S. (eds) Theory and Applications of Satisfiability Testing – SAT 2010. SAT 2010. Lecture Notes in Computer Science, vol 6175. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14186-7_8

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  • DOI: https://doi.org/10.1007/978-3-642-14186-7_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14185-0

  • Online ISBN: 978-3-642-14186-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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