Summary: Synthesizing Shortest Linear Straight-Line
Programs over GF(2) using SAT
and Peter Schneider-Kamp2
LuFG Informatik 2, RWTH Aachen University, Germany
IMADA, University of Southern Denmark, Denmark
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 -approximation for the problem unless P = NP.
This paper presents a non-approximative approach for finding the short-
est 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.