TY - GEN

T1 - Synthesizing shortest linear straight-line programs over GF(2) using SAT

AU - Fuhs, Carsten

AU - Schneider-Kamp, Peter

PY - 2010/8/2

Y1 - 2010/8/2

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=77954969533&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-14186-7_8

DO - 10.1007/978-3-642-14186-7_8

M3 - Article in proceedings

AN - SCOPUS:77954969533

SN - 3642141854

SN - 9783642141850

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 71

EP - 84

BT - Theory and Applications of Satisfiability Testing - 13th International Conference, SAT 2010, Proceedings

T2 - 13th International Conference on Theory and Applications of Satisfiability Testing, SAT 2010

Y2 - 11 July 2010 through 14 July 2010

ER -