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25
A Knowledge Compilation Map
 Journal of Artificial Intelligence Research
, 2002
"... We propose a perspective on knowledge compilation which calls for analyzing different compilation approaches according to two key dimensions: the succinctness of the target compilation language, and the class of queries and transformations that the language supports in polytime. ..."
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Cited by 162 (24 self)
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We propose a perspective on knowledge compilation which calls for analyzing different compilation approaches according to two key dimensions: the succinctness of the target compilation language, and the class of queries and transformations that the language supports in polytime.
A Survey on Knowledge Compilation
, 1998
"... this paper we survey recent results in knowledge compilation of propositional knowledge bases. We first define and limit the scope of such a technique, then we survey exact and approximate knowledge compilation methods. We include a discussion of compilation for nonmonotonic knowledge bases. Keywor ..."
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Cited by 95 (3 self)
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this paper we survey recent results in knowledge compilation of propositional knowledge bases. We first define and limit the scope of such a technique, then we survey exact and approximate knowledge compilation methods. We include a discussion of compilation for nonmonotonic knowledge bases. Keywords: Knowledge Representation, Efficiency of Reasoning
Automated Reasoning and Exhaustive Search: Quasigroup Existence Problems
, 1995
"... this paper we consider only exhaustive searching techniques rather than more radical ones such as genetic algorithms, simulated annealing or the like. Among search algorithms, we consider only backtracking methods to which the cardinality of the constraints is irrelevant. This narrowing of our focu ..."
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Cited by 56 (4 self)
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this paper we consider only exhaustive searching techniques rather than more radical ones such as genetic algorithms, simulated annealing or the like. Among search algorithms, we consider only backtracking methods to which the cardinality of the constraints is irrelevant. This narrowing of our focus is in no way intended to slight any of the alternative methods. Merely, our research is what it is and not another thing. It is extremely easy and natural to represent existence problems such as our QG1QG7 in terms of consistent labelling. To generate a quasigroup of order v is to fill in each of the v
Implementing the DavisPutnam Method
 Journal of Automated Reasoning
, 2000
"... The method proposed by Davis, Putnam, Logemann, and Loveland for propositional reasoning, often referred to as the DavisPutnam method, is one of the major practical methods for the satisfiability (SAT) problem of propositional logic. We show how to implement the DavisPutnam method efficiently usin ..."
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Cited by 53 (3 self)
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The method proposed by Davis, Putnam, Logemann, and Loveland for propositional reasoning, often referred to as the DavisPutnam method, is one of the major practical methods for the satisfiability (SAT) problem of propositional logic. We show how to implement the DavisPutnam method efficiently using the trie data structure for propositional clauses. A new technique of indexing only the first and last literals of clauses yields a unit propagation procedure whose complexity is sublinear to the number of occurrences of the variable in the input. We also show that the DavisPutnam method can work better when unit subsumption is not used. We illustrate the performance of our programs on some quasigroup problems. The efficiency of our programs has enabled us to solve some open quasigroup problems.
Tractable Databases: How to Make Propositional Unit Resolution Complete through Compilation
, 1994
"... We present procedures to compile any propositional clausal database \Sigma into a logically equivalent "compiled" database \Sigma ? such that, for any clause C, \Sigma j= C if and only if there is a unit refutation of \Sigma ? [ :C. It follows that once the compilation process is complete any qu ..."
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Cited by 38 (5 self)
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We present procedures to compile any propositional clausal database \Sigma into a logically equivalent "compiled" database \Sigma ? such that, for any clause C, \Sigma j= C if and only if there is a unit refutation of \Sigma ? [ :C. It follows that once the compilation process is complete any query about the logical consequences of \Sigma can be correctly answered in time linear in the sum of the sizes of \Sigma ? and the query. The compiled database \Sigma ? is for all but one of the procedures a subset of the set P I (\Sigma) of prime implicates of \Sigma, but \Sigma ? can be exponentially smaller than P I (\Sigma). Of independent interest, we prove the equivalence of unitrefutability with two restrictions of resolution, and provide a new sufficient condition for unit refutation completeness, thus identifying a new class of tractable theories, one which is of interest to abduction problems as well. Finally, we apply the results to the design of a complete LTMS. 1 INTRODUCT...
Implementing the DavisPutnam Algorithm by Tries
 ARTIFICIAL INTELLIGENCE CENTER, SRI INTERNATIONAL, MENLO
, 1994
"... The DavisPutnam method is one of the major practical methods for the satisfiability (SAT) problem of propositional logic. We show how to implement the DavisPutnam method efficiently using the trie data structure for propositional clauses by presenting seven implementations of the method. We prop ..."
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Cited by 37 (7 self)
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The DavisPutnam method is one of the major practical methods for the satisfiability (SAT) problem of propositional logic. We show how to implement the DavisPutnam method efficiently using the trie data structure for propositional clauses by presenting seven implementations of the method. We propose a new technique for implementing unit propagation whose complexity is sublinear to the number of occurrences of the variable in the input. We present the performance of our programs on some quasigroup problems. The efficiency of our programs allowed us to solve some open quasigroup problems.
MultiResolution on Compressed Sets of Clauses
 Proc. of 12th International Conference on Tools with Artificial Intelligence (ICTAI2000
, 2000
"... This paper presents a system based on new operators for handling sets of propositional clauses represented by means of ZBDDs. The high compression power of such data structures allows efficient encodings of structured instances. A specialized operator for the distribution of sets of clauses is intro ..."
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Cited by 31 (4 self)
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This paper presents a system based on new operators for handling sets of propositional clauses represented by means of ZBDDs. The high compression power of such data structures allows efficient encodings of structured instances. A specialized operator for the distribution of sets of clauses is introduced and used for performing multiresolution on clause sets. Cut eliminations between sets of clauses of exponential size may then be performed using polynomial size data structures. The ZRES system, a new implementation of the DavisPutnam procedure of 1960, solves two hard problems for resolution, that are currently out of the scope of the best SAT provers. 1
Open World Planning in the Situation Calculus
 In Proceedings of the 7th Conference on Artificial Intelligence (AAAI00) and of the 12th Conference on Innovative Applications of Artificial Intelligence (IAAI00
, 1999
"... We describe a forward reasoning planner for open worlds that uses domain specific information for pruning its search space, as suggested by (Bacchus & Kabanza 1996; 2000). The planner is written in the situation calculusbased programming language GOLOG, and it uses a situation calculus axiomat ..."
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Cited by 28 (2 self)
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We describe a forward reasoning planner for open worlds that uses domain specific information for pruning its search space, as suggested by (Bacchus & Kabanza 1996; 2000). The planner is written in the situation calculusbased programming language GOLOG, and it uses a situation calculus axiomatization of the application domain. Given a sentence oe to prove, the planner regresses it to an equivalent sentence oe 0 about the initial situation, then invokes a theorem prover to determine whether the initial database entails oe 0 and hence oe. We describe two approaches to this theorem proving task, one based on compiling the initial database to prime implicate form, the other based on Relsat, a Davis/Putnambased procedure. Finally, we report on our experiments with open world planning based on both these approaches to the theorem proving task.
A New Method for Consequence Finding and Compilation in Restricted Languages
, 1999
"... SFK (skipfiltered, kernel) resolution is a new method for finding "interesting" consequences of a first order clausal theory \Sigma, namely those in some restricted target language LT . In its more restrictive form, SFK resolution corresponds to a relatively efficient SAT method, directional resolu ..."
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Cited by 22 (4 self)
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SFK (skipfiltered, kernel) resolution is a new method for finding "interesting" consequences of a first order clausal theory \Sigma, namely those in some restricted target language LT . In its more restrictive form, SFK resolution corresponds to a relatively efficient SAT method, directional resolution; in its more general form, to a full prime implicate algorithm, namely Tison 's. It generalizes both of them by offering much more flexible search, first order completeness, and a much wider range of inferential capabilities. SFK resolution has many applications: computing "characteristic" clauses for taskspecific languages in abduction, explanation and nonmonotonic reasoning (Inoue 1992); obtaining LUB approximations of the input theory (Selman and Kautz 1996) which are of polynomial size; incremental and lazy exact knowledge compilation (del Val 1994); and compilation into a tractable form for restricted target languages, independently of the tractability of inference in the given ...
Implicates and Prime Implicates in Random 3SAT
 Artificial Intelligence
, 1995
"... It has been observed previously that Random 3SAT exhibits a phase transition at a critical ratio of constraints to variables, where the average frequency of satisfiability falls abruptly from near 1 to near 0. In this paper we look beyond satisfiability to implicates and prime implicates of nonzero ..."
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Cited by 21 (0 self)
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It has been observed previously that Random 3SAT exhibits a phase transition at a critical ratio of constraints to variables, where the average frequency of satisfiability falls abruptly from near 1 to near 0. In this paper we look beyond satisfiability to implicates and prime implicates of nonzero length and show experimentally that, for any given length, these exhibit their own phase transitions. All of these phase transitions appear to share the same critical point as the wellknown satisfiability phase transition. We also find a rich, regular Some of this work was done while the first author was in the Qualitative Reasoning Group at the Artificial Intelligence Laboratory, the University of Texas at Austin, at a time when the Qualitative Reasoning Group was supported in part by NSF grants IRI8904454, IRI9017047, and IRI9216584, and by NASA contracts NCC 2760 and NAG 9665. Some of this work also was done while the first author was at AT&T Bell Laboratories. y The second au...