CSE-TR-292-96 - GRASPA New Search Algorithm for...

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CSE-TR- GRASP—A New Search Algorithm for Satisfiability João P. Marques Silva Karem A. Sakallah 292-96 Computer Science and Engineering Division Department of Electrical Engineering and Computer Science Ann Arbor, Michigan 48109-2122 USA THE UNIVERSITY OF MICHIGAN April 10, 1996
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GRASP—A New Search Algorithm for Satisfiability João P. Marques Silva Karem A. Sakallah Advanced Computer Architecture Laboratory Department of Electrical Engineering and Computer Science University of Michigan Ann Arbor, Michigan 48109-2122 April 10, 1996
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Abstract This report introduces GRASP (Generic seaRch Algorithm for the Satisfiability Problem), an integrated algorithmic frame- work for SAT that unifies several previously proposed search-pruning techniques and facilitates identification of additional ones. GRASP is premised on the inevitability of conflicts during search and its most distinguishing feature is the augmentation of basic backtracking search with a powerful conflict analysis procedure. Analyzing conflicts to determine their causes enables GRASP to backtrack non-chronologically to earlier levels in the search tree, potentially pruning large portions of the search space. In addition, by “recording” the causes of conflicts, GRASP can recognize and preempt the occurrence of similar con- flicts later on in the search. Finally, straightforward bookkeeping of the causality chains leading up to conflicts allows GRASP to identify assignments that are necessary for a solution to be found. Experimental results obtained from a large number of benchmarks, including many from the field of test pattern generation, indicate that application of the proposed conflict analy- sis techniques to SAT algorithms can be extremely effective for a large number of representative classes of SAT instances.
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CSE-TR-292-96: GRASP—A New Search Algorithm for Satisfiability 1 1 Introduction The Boolean satisfiability problem (SAT) appears in many contexts in the field of computer-aided design of integrated cir- cuits including automatic test pattern generation (ATPG), timing analysis, delay fault testing, and logic verification, to name just a few. Though well-researched and widely investigated, it remains the focus of continuing interest because efficient tech- niques for its solution can have great impact. SAT belongs to the class of NP-complete problems whose algorithmic solutions are currently believed to have exponential worst case complexity [11] . Over the years, many algorithmic solutions have been proposed for SAT, the most well known being the different variations of the Davis-Putnam procedure [5] . The best known ver- sion of this procedure is based on a backtracking search algorithm that, at each node in the search tree, elects an assignment and prunes subsequent search by iteratively applying the unit clause and the pure literal rules [30] . Iterated application of the unit clause rule is commonly referred to as Boolean Constraint Propagation (BCP) [30] or as derivation of implications in the electronic CAD literature [1] .
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