Summary: Solving Difficult SAT Instances in the Presence of Symmetry
Fadi A. Aloul, Arathi Ramani, Igor L. Markov and Karem A. Sakallah
Department of EECS, University of Michigan, Ann Arbor 48109-2122
Research in algorithms for Boolean satisfiability and their implementa-
tions [23, 6] has recently outpaced benchmarking efforts. Most of the
classic DIMACS benchmarks  can be solved in seconds on commod-
ity PCs. More recent benchmarks take longer to solve because of their
large size, but are still solved in minutes . Yet, small and difficult
SAT instances must exist because Boolean satisfiability is NP-complete.
We propose an improved construction of symmetry-breaking clauses
 and apply it to achieve significant speed-ups over current state-of-
the-art in Boolean satisfiability. Our techniques are formulated as pre-
processing and can be applied to any SAT solver without changing its
source code. We also show that considerations of symmetry may lead to
more efficient reductions to SAT in the routing domain.
Our work articulates SAT instances that are unusually difficult for
their size, including satisfiable instances derived from routing problems.
Using an efficient implementation to solve the graph automorphism prob-