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IEEE TRANSACTIONS ON COMPUTER-AIDED DESIGN OF INTEGRATED CIRCUITS AND SYSTEMS, VOL. 22, NO. 9, SEPTEMBER 2003 1117 Solving Difficult Instances of Boolean Satisfiability
 

Summary: IEEE TRANSACTIONS ON COMPUTER-AIDED DESIGN OF INTEGRATED CIRCUITS AND SYSTEMS, VOL. 22, NO. 9, SEPTEMBER 2003 1117
Solving Difficult Instances of Boolean Satisfiability
in the Presence of Symmetry
Fadi A. Aloul, Student Member, IEEE, Arathi Ramani, Igor L. Markov, and Karem A. Sakallah, Fellow, IEEE
Abstract--Research in algorithms for Boolean satisfiability
(SAT) and their implementations (Goldberg and Novikov, 2002),
(Moskewicz et al., 2001), (Silva and Sakallah, 1999) has recently
outpaced benchmarking efforts. Most of the classic DIMACS
benchmarks (ftp:dimacs.rutgers.edu/pub/challenge/sat/bench-
marks/cnf) can now be solved in seconds on commodity PCs. More
recent benchmarks (Velev and Bryant, 2001) take longer to solve
due to their large size, but are still solved in minutes. Yet, relatively
small and difficult SAT instances must exist if P = NP. To
this end, our paper articulates SAT instances that are unusually
difficult for their size, including satisfiable instances derived
from very large scale integration (VLSI) routing problems. With
an efficient implementation to solve the graph automorphism
problem (McKay, 1990), (Soicher, 1993), (Spitznagel, 1994), we
show that in structured SAT instances, difficulty may be associated
with large numbers of symmetries. We point out that a previously

  

Source: Aloul, Fadi - Department of Computer Engineering, American University of Sharjah
Markov, Igor - Department of Electrical Engineering and Computer Science, University of Michigan

 

Collections: Computer Technologies and Information Sciences; Engineering