 
Summary: Synthesizing Shortest Linear StraightLine
Programs over GF(2) using SAT
Carsten Fuhs1
and Peter SchneiderKamp2
1
LuFG Informatik 2, RWTH Aachen University, Germany
fuhs@informatik.rwthaachen.de
2
IMADA, University of Southern Denmark, Denmark
petersk@imada.sdu.dk
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 approximation for the problem unless P = NP.
This paper presents a nonapproximative approach for finding the short
est 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.
