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Solving Difficult SAT Instances in the Presence of Symmetry

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
faloul,ramania,imarkov,karem @umich.edu
Research in algorithms for Boolean satisfiability and their efficient
implementations [26, 8] has recently outpaced benchmarking ef-
forts. Most of the classic DIMACS benchmarks from the early
1990s [12] can be solved in seconds on commodity PCs. More
recent benchmarks take longer to solve primarily because of their
large size, but are still solved in minutes [28]. However, small and
difficult SAT instances must exist because Boolean satisfiability is
Our work articulates a number of SAT instances that are un-
usually difficult for their size, including satisfiable instances from
global routing and detailed routing for FPGAs [22]. Using an ef-
ficient implementation to solve the graph automorphism problem
[21, 23, 25], we show that in structured SAT instances difficulty is
sometimes associated with large numbers of symmetries.


Source: Aloul, Fadi - Department of Computer Engineering, American University of Sharjah


Collections: Engineering