NDLI: Solving difficult instances of Boolean satisfiability in the presence of symmetry

Content Provider	IEEE Xplore Digital Library
Author	Aloul, F.A. Ramani, A. Markov, I.L. Sakallah, K.A.
Copyright Year	1982
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/benchmarks/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 /spl ne/ 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 published symmetry extraction mechanism (Crawford et al., 1996) based on a reduction to the graph automorphism problem often produces many spurious symmetries. Our paper contributes two new reductions to graph automorphism, which extract all correct symmetries found previously (Crawford et al., 1996) as well as phase-shift symmetries not found earlier. The correctness of our reductions is rigorously proven, and they are evaluated empirically. We also formulate an improved construction of symmetry-breaking clauses in terms of permutation cycles and propose to use only generators of symmetries in this process. These ideas are implemented in a fully automated flow that first extracts symmetries from a given SAT instance, preprocesses it by adding symmetry-breaking clauses, and then calls a state-of-the-art backtrack SAT solver. Significant speed-ups are shown on many benchmarks versus direct application of the solver. In an attempt to further improve the practicality of our approach, we propose a scheme for fast "opportunistic" symmetry extraction and also show that considerations of symmetry may lead to more efficient reductions to SAT in the VLSI routing domain.
Sponsorship	IEEE Council on Electronic Design Automation IEEE Circuits and Systems Society
Starting Page	1117
Ending Page	1137
Page Count	21
File Size	1110683
File Format	PDF
ISSN	02780070
Volume Number	22
Issue Number	9
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2003-09-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Very large scale integration Personal communication networks Routing Design automation Polynomials Application software Logic Microprocessors Silicon Field programmable gate arrays
Content Type	Text
Resource Type	Article
Subject	Computer Graphics and Computer-Aided Design Electrical and Electronic Engineering Software

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

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