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Synthesizing shortest linear straightline programs over GF(2) using SAT
 In Proc. SAT ’10, volume 6175 of LNCS
, 2010
"... Abstract. Nontrivial linear straightline programs over the Galois field of two elements occur frequently in applications such as encryption or highperformance computing. Finding the shortest linear straightline program for a given set of linear forms is known to be MaxSNPcomplete, i.e., there i ..."
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Abstract. Nontrivial linear straightline programs over the Galois field of two elements occur frequently in applications such as encryption or highperformance computing. Finding the shortest linear straightline program for a given set of linear forms is known to be MaxSNPcomplete, i.e., there is no ǫapproximation for the problem unless P = NP. This paper presents a nonapproximative approach for finding the shortest linear straightline 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. 1