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54
Stable models and an alternative logic programming paradigm
 In The Logic Programming Paradigm: a 25Year Perspective
, 1999
"... In this paper we reexamine the place and role of stable model semantics in logic programming and contrast it with a least Herbrand model approach to Horn programs. We demonstrate that inherent features of stable model semantics naturally lead to a logic programming system that offers an interesting ..."
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Cited by 289 (18 self)
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In this paper we reexamine the place and role of stable model semantics in logic programming and contrast it with a least Herbrand model approach to Horn programs. We demonstrate that inherent features of stable model semantics naturally lead to a logic programming system that offers an interesting alternative to more traditional logic programming styles of Horn logic programming, stratified logic programming and logic programming with wellfounded semantics. The proposed approach is based on the interpretation of program clauses as constraints. In this setting programs do not describe a single intended model, but a family of stable models. These stable models encode solutions to the constraint satisfaction problem described by the program. Our approach imposes restrictions on the syntax of logic programs. In particular, function symbols are eliminated from the language. We argue that the resulting logic programming system is wellattuned to problems in the class NP, has a welldefined domain of applications, and an emerging methodology of programming. We point out that what makes the whole approach viable is recent progress in implementations of algorithms to compute stable models of propositional logic programs. 1
Knowledge compilation and theory approximation
 Journal of the ACM
, 1996
"... Computational efficiency is a central concern in the design of knowledge representation systems. In order to obtain efficient systems, it has been suggested that one should limit the form of the statements in the knowledge base or use an incomplete inference mechanism. The former approach is often t ..."
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Cited by 184 (5 self)
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Computational efficiency is a central concern in the design of knowledge representation systems. In order to obtain efficient systems, it has been suggested that one should limit the form of the statements in the knowledge base or use an incomplete inference mechanism. The former approach is often too restrictive for practical applications, whereas the latter leads to uncertainty about exactly what can and cannot be inferred from the knowledge base. We present a third alternative, in which knowledge given in a general representation language is translated (compiled) into a tractable form — allowing for efficient subsequent query answering. We show how propositional logical theories can be compiled into Horn theories that approximate the original information. The approximations bound the original theory from below and above in terms of logical strength. The procedures are extended to other tractable languages (for example, binary clauses) and to the firstorder case. Finally, we demonstrate the generality of our approach by compiling concept descriptions in a general framebased language into a tractable form.
Finding Hard Instances of the Satisfiability Problem: A Survey
, 1997
"... . Finding sets of hard instances of propositional satisfiability is of interest for understanding the complexity of SAT, and for experimentally evaluating SAT algorithms. In discussing this we consider the performance of the most popular SAT algorithms on random problems, the theory of average case ..."
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Cited by 125 (1 self)
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. Finding sets of hard instances of propositional satisfiability is of interest for understanding the complexity of SAT, and for experimentally evaluating SAT algorithms. In discussing this we consider the performance of the most popular SAT algorithms on random problems, the theory of average case complexity, the threshold phenomenon, known lower bounds for certain classes of algorithms, and the problem of generating hard instances with solutions.
The SAT Phase Transition
, 1994
"... : We describe a detailed experimental investigation of the phase transition for several different classes of randomly generated satisfiability problems. We observe a remarkable consistency of features in the phase transition despite the presence in some of the problem classes of clauses of mixed len ..."
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Cited by 65 (8 self)
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: We describe a detailed experimental investigation of the phase transition for several different classes of randomly generated satisfiability problems. We observe a remarkable consistency of features in the phase transition despite the presence in some of the problem classes of clauses of mixed lengths. For instance, each of the problem classes considered has a sharp transition from satisfiable to unsatisfiable problems at a critical value. In addition, there is a common easyhard easy pattern in the difficulty of the problems, with the hardest problems being associated with the phase transition. However, the difficulty of problems of mixed clause lengths is much more variable than that of fixed clause length. Indeed, whilst the median difficulty of random problems of mixed clause lengths can be orders of magnitude easier than that of equivalently sized problems of fixed clause length, the hardest problems of mixed clause lengths can be orders of magnitude harder than the hardest equi...
Conflict analysis in search algorithms for propositional satisfiability
 in Proceedings of the IEEE International Conference on Tools with Artificial Intelligence
, 1996
"... This paper introduces GRASP (Generic seaRch Algorithm for the Sati$ability Problem), a new search algorithm for Propositional Satisjability (SAT). GRASP incorporates several searchpruning techniques, some of which are spec$c to SAT whereas others find equivalent in other fieh ofArt$cial Intelligenc ..."
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Cited by 54 (2 self)
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This paper introduces GRASP (Generic seaRch Algorithm for the Sati$ability Problem), a new search algorithm for Propositional Satisjability (SAT). GRASP incorporates several searchpruning techniques, some of which are spec$c to SAT whereas others find equivalent in other fieh ofArt$cial Intelligence. GRASP is premised on the inevitability of conflicts during search and its most distinguishing feature is the augmentation of basic backtracking search with a
Tabu Search for SAT
 In Proceedings of AAAI’97
"... In this paper, tabu search for SAT is investigated from an experimental point of view. To this end, TSAT, a basic tabu search algorithm for SAT, is introduced and compared with Selman et al. Random Walk Strategy GSAT procedure, in short RWSGSAT. TSAT does not involve the additional ..."
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Cited by 48 (2 self)
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In this paper, tabu search for SAT is investigated from an experimental point of view. To this end, TSAT, a basic tabu search algorithm for SAT, is introduced and compared with Selman et al. Random Walk Strategy GSAT procedure, in short RWSGSAT. TSAT does not involve the additional
Computing With Default Logic
, 1999
"... Default logic was proposed by Reiter as a knowledge representation tool. In this paper, we present our work on the Default Reasoning System, DeReS, the first comprehensive and optimized implementation of default logic. While knowledge representation remains the main application area for default l ..."
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Cited by 38 (6 self)
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Default logic was proposed by Reiter as a knowledge representation tool. In this paper, we present our work on the Default Reasoning System, DeReS, the first comprehensive and optimized implementation of default logic. While knowledge representation remains the main application area for default logic, as a source of largescale problems needed for experimentation and as a source of intuitions needed for a systematic methodology of encoding problems as default theories we use here the domain of combinatorial problems. To experimentally study the performance of DeReS we developed a benchmarking system, the TheoryBase. The TheoryBase is designed to support experimental investigations of nonmonotonic reasoning systems based on the language of default logic or logic programming. It allows the user to create parameterized collections of default theories having similar properties and growing sizes and, consequently, to study the asymptotic performance of nonmonotonic systems under i...
The Satisfiability Constraint Gap
 Artificial Intelligence
, 1996
"... We describe an experimental investigation of the satisfiability phase transition for several different classes of randomly generated problems. We show that the "conventional" picture of easyhardeasy problem difficulty is inadequate. In particular, there is a region of very variable probl ..."
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Cited by 33 (10 self)
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We describe an experimental investigation of the satisfiability phase transition for several different classes of randomly generated problems. We show that the "conventional" picture of easyhardeasy problem difficulty is inadequate. In particular, there is a region of very variable problem difficulty where problems are typically underconstrained and satisfiable. Within this region, problems can be orders of magnitude harder than problems in the middle of the satisfiability phase transition. These extraordinary hard problems appear to be associated with a constraint gap, a minimum in the amount of constraint propagation compared to the amount of search. We show that the position and shape of this constraint gap are very consistent with problem size. Unlike hard problems in the middle of satisfiability phase transition, hard problems in the variable region are not critically constrained between satisfiability and unsatisfiability. Indeed, hard problems in the variable region often cont...
The Hardest Random SAT Problems
 In Proceedings, KI94
, 1994
"... : We describe a detailed experimental investigation of the phase transition for several different classes of satisfiability problems including random kSAT, the constant probability model, and encodings of kcolourability and the independent set problem. We show that the conventional picture of eas ..."
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Cited by 23 (7 self)
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: We describe a detailed experimental investigation of the phase transition for several different classes of satisfiability problems including random kSAT, the constant probability model, and encodings of kcolourability and the independent set problem. We show that the conventional picture of easyhardeasy behaviour is inadequate. In each of the problem classes, although median problem difficulty shows an easyhardeasy pattern, there is also a region of very variable problem difficulty. Within this region, we have found problems orders of magnitude harder than those in the middle of the phase transition. These extraordinary problems can easily dominate the mean problem difficulty. We report experimental evidence which strongly suggests that this behaviour is due to a "constraint gap", a region where the number of constraints on variables is minimal while simultaneously the depth of search required to solve problems is maximal. We also report results suggesting that better algorith...
Comparative Studies of Constraint Satisfaction and DavisPutnam Algorithms for Maximum Satisfiability Problems
 Cliques, Coloring and Satisfiability
"... Maximum satisfiability (MAXSAT) is an extension of satisfiability (SAT), in which a partial solution is sought that satisfies the maximum number of clauses in a logical formula. Enumerative methods giving guaranteed optimal solutions can be derived from traditional search algorithms used to solve S ..."
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Cited by 19 (0 self)
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Maximum satisfiability (MAXSAT) is an extension of satisfiability (SAT), in which a partial solution is sought that satisfies the maximum number of clauses in a logical formula. Enumerative methods giving guaranteed optimal solutions can be derived from traditional search algorithms used to solve SAT problems, in particular the Davis Putnam procedure. Algorithms have also been developed for the maximal constraint satisfaction problem (MAXCSP), a generalization of MAXSAT, that are extensions of search algorithms used to solve constraint satisfaction problems. In the present work, these algorithms were compared over the same sets of problems, using comparable implementations. In addition, variants of each algorithm were tested to determine the contribution of component strategies that often make up a working algorithm. The componential analysis was done using traditional multifactor experimental designs in which the effect of different strategies could be studied at the same time th...