The Experts below are selected from a list of 978 Experts worldwide ranked by ideXlab platform
Eliezer L. Lozinskii - One of the best experts on this subject based on the ideXlab platform.
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the good old Davis Putnam Procedure helps counting models
arXiv: Artificial Intelligence, 2011Co-Authors: Elazar Birnbaum, Eliezer L. LozinskiiAbstract:As was shown recently, many important AI problems require counting the number of models of propositional formulas. The problem of counting models of such formulas is, according to present knowledge, computationally intractable in a worst case. Based on the Davis-Putnam Procedure, we present an algorithm, CDP, that computes the exact number of models of a propositional CNF or DNF formula F. Let m and n be the number of clauses and variables of F, respectively, and let p denote the probability that a literal l of F occurs in a clause C of F, then the average running time of CDP is shown to be O(nm^d), where d=-1/log(1-p). The practical performance of CDP has been estimated in a series of experiments on a wide variety of CNF formulas.
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The Good Old Davis-Putnam Procedure Helps Counting Models
1999Co-Authors: Elazar Birnbaum, Eliezer L. LozinskiiAbstract:As was shown recently, many important AI problems require counting the number of models of propositional formulas. The problem of counting models of such formulas is, according to present knowledge, computationally intractable in a worst case. Based on the Davis-Putnam Procedure, we present an algorithm, CDP, that computes the exact number of models of a propositional CNF or DNF formula F. Let m and n be the number of clauses and variables of F, respectively, and let p denote the probability that a literal l of F occurs in a clause C of F, then the average running time of CDP is shown to be O(m d n), where d = d 1 lo
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The Good Old Davis-Putnam Procedure Helps Counting Models
1999Co-Authors: Elazar Birnbaum, Eliezer L. LozinskiiAbstract:As was shown recently, many important AI problems require counting the number of models of propositional formulas. The problem of counting models of such formulas is, according to present knowledge, computationally intractable in a worst case. Based on the Davis-Putnam Procedure, we present an algorithm, CDP, that computes the exact number of models of a propositional CNF or DNF formula F . Let m and n be the number of clauses and variables of F , respectively, and let p denote the probability that a literal l of F occurs in a clause C of F , then the average running time of CDP is shown to be O(m d n), where d = d \Gamma1 log 2 (1\Gammap) e. The practical performance of CDP has been estimated in a series of experiments on a wide variety of CNF formulas. 1. Introduction Given a propositional formula F in CNF or DNF, one may want to know what is the number (F ) of its models, that is, assignments of truth values to its variables that satisfy F . This problem of counting models ..
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The Good Old Davis-Putnam . . .
1999Co-Authors: Elazar Birnbaum, Eliezer L. LozinskiiAbstract:As was shown recently, many important AI problems require counting the number of models of propositional formulas. The problem of counting models of such formulas is, according to present knowledge, computationally intractable in a worst case. Based on the Davis-Putnam Procedure, we present an algorithm, CDP, that computes the exact number of models of a propositional CNF or DNF formula F . Let m and n be the number of clauses and variables of F , respectively, and let p denote the probability that a literal l of F occurs in a clause C of F , then the average running time of CDP is shown to be O(m n), where d = d e. The practical performance of CDP has been estimated in a series of experiments on a wide variety of CNF formulas
Niklas Eén - One of the best experts on this subject based on the ideXlab platform.
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symbolic reachability analysis based on sat solvers
Tools and Algorithms for Construction and Analysis of Systems, 2000Co-Authors: Parosh Aziz Abdulla, Per Bjesse, Niklas EénAbstract:The introduction of symbolic model checking using Binary Decision Diagrams (BDDs) has led to a substantial extension of the class of systems that can be algorithmically verified. Although BDDs have played a crucial role in this success, they have some well-known drawbacks, such as requiring an externally supplied variable ordering and causing space blowups in certain applications. In a parallel development, SAT-solving Procedures, such as Stalmarck's method or the Davis-Putnam Procedure, have been used successfully in verifying very large industrial systems. These efforts have recently attracted the attention of the model checking community resulting in the notion of bounded model checking. In this paper, we show how to adapt standard algorithms for symbolic reachability analysis to work with SAT-solvers. The key element of our contribution is the combination of an algorithm that removes quantifiers over propositional variables and a simple representation that allows reuse of subformulas. The result will in principle allow many existing BDD-based algorithms to work with SAT-solvers. We show that even with our relatively simple techniques it is possible to verify systems that are known to be hard for BDD-based model checkers.
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Symbolic Reachability Analysis based on SAT Solvers
2000Co-Authors: Parosh Aziz Abdulla, Per Bjesse, Niklas EénAbstract:. The introduction of symbolic model checking using Binary Decision Diagrams (BDDs) has led to a substantial extension of the class of systems which can be algorithmically verified. Although BDDs have played a crucial role in this success they have some well-known drawbacks, such as requiring an externally supplied variable ordering and causing space blowups in certain applications. In a parallel development, SAT solving Procedures, such as Stalmarck's method or the Davis-Putnam Procedure, have been used successfully in verifying very large industrial systems. These efforts have recently attracted the attention of the model checking community resulting in the notion of bounded model checking. In this paper, we show how to adapt standard algorithms for symbolic reachability analysis to work with SAT-solvers. The key element of our contribution is the combination of an algorithm that removes quantifiers over propositional variables and a simple representation that allows re..
Nobuhiro Yugami - One of the best experts on this subject based on the ideXlab platform.
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theoretical analysis of Davis Putnam Procedure and propositional satisfiability
International Joint Conference on Artificial Intelligence, 1995Co-Authors: Nobuhiro YugamiAbstract:This paper presents a statistical analysis of the Davis-Putnam Procedure and propositional satisfiability problems (SAT). SAT has been researched in AI because of its strong relationship to automated reasoning and recently it is used as a benchmark problem of constraint satisfaction algorithms. The Davis-Putnam Procedure is a well-known satisfiability checking algorithm based on tree search technique. In this paper, I analyze two average case complexities for the Davis-Putnam Procedure, the complexity for satisfiability checking and the complexity for finding all solutions. I also discuss the probability of satisfiability. The complexities and the probability strongly depend on the distribution of formulas to be tested and I use the fixed clause length model as the distribution model. The result of the analysis coincides with the experimental result well.
Elazar Birnbaum - One of the best experts on this subject based on the ideXlab platform.
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the good old Davis Putnam Procedure helps counting models
arXiv: Artificial Intelligence, 2011Co-Authors: Elazar Birnbaum, Eliezer L. LozinskiiAbstract:As was shown recently, many important AI problems require counting the number of models of propositional formulas. The problem of counting models of such formulas is, according to present knowledge, computationally intractable in a worst case. Based on the Davis-Putnam Procedure, we present an algorithm, CDP, that computes the exact number of models of a propositional CNF or DNF formula F. Let m and n be the number of clauses and variables of F, respectively, and let p denote the probability that a literal l of F occurs in a clause C of F, then the average running time of CDP is shown to be O(nm^d), where d=-1/log(1-p). The practical performance of CDP has been estimated in a series of experiments on a wide variety of CNF formulas.
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The Good Old Davis-Putnam Procedure Helps Counting Models
1999Co-Authors: Elazar Birnbaum, Eliezer L. LozinskiiAbstract:As was shown recently, many important AI problems require counting the number of models of propositional formulas. The problem of counting models of such formulas is, according to present knowledge, computationally intractable in a worst case. Based on the Davis-Putnam Procedure, we present an algorithm, CDP, that computes the exact number of models of a propositional CNF or DNF formula F. Let m and n be the number of clauses and variables of F, respectively, and let p denote the probability that a literal l of F occurs in a clause C of F, then the average running time of CDP is shown to be O(m d n), where d = d 1 lo
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The Good Old Davis-Putnam Procedure Helps Counting Models
1999Co-Authors: Elazar Birnbaum, Eliezer L. LozinskiiAbstract:As was shown recently, many important AI problems require counting the number of models of propositional formulas. The problem of counting models of such formulas is, according to present knowledge, computationally intractable in a worst case. Based on the Davis-Putnam Procedure, we present an algorithm, CDP, that computes the exact number of models of a propositional CNF or DNF formula F . Let m and n be the number of clauses and variables of F , respectively, and let p denote the probability that a literal l of F occurs in a clause C of F , then the average running time of CDP is shown to be O(m d n), where d = d \Gamma1 log 2 (1\Gammap) e. The practical performance of CDP has been estimated in a series of experiments on a wide variety of CNF formulas. 1. Introduction Given a propositional formula F in CNF or DNF, one may want to know what is the number (F ) of its models, that is, assignments of truth values to its variables that satisfy F . This problem of counting models ..
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The Good Old Davis-Putnam . . .
1999Co-Authors: Elazar Birnbaum, Eliezer L. LozinskiiAbstract:As was shown recently, many important AI problems require counting the number of models of propositional formulas. The problem of counting models of such formulas is, according to present knowledge, computationally intractable in a worst case. Based on the Davis-Putnam Procedure, we present an algorithm, CDP, that computes the exact number of models of a propositional CNF or DNF formula F . Let m and n be the number of clauses and variables of F , respectively, and let p denote the probability that a literal l of F occurs in a clause C of F , then the average running time of CDP is shown to be O(m n), where d = d e. The practical performance of CDP has been estimated in a series of experiments on a wide variety of CNF formulas
Parosh Aziz Abdulla - One of the best experts on this subject based on the ideXlab platform.
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symbolic reachability analysis based on sat solvers
Tools and Algorithms for Construction and Analysis of Systems, 2000Co-Authors: Parosh Aziz Abdulla, Per Bjesse, Niklas EénAbstract:The introduction of symbolic model checking using Binary Decision Diagrams (BDDs) has led to a substantial extension of the class of systems that can be algorithmically verified. Although BDDs have played a crucial role in this success, they have some well-known drawbacks, such as requiring an externally supplied variable ordering and causing space blowups in certain applications. In a parallel development, SAT-solving Procedures, such as Stalmarck's method or the Davis-Putnam Procedure, have been used successfully in verifying very large industrial systems. These efforts have recently attracted the attention of the model checking community resulting in the notion of bounded model checking. In this paper, we show how to adapt standard algorithms for symbolic reachability analysis to work with SAT-solvers. The key element of our contribution is the combination of an algorithm that removes quantifiers over propositional variables and a simple representation that allows reuse of subformulas. The result will in principle allow many existing BDD-based algorithms to work with SAT-solvers. We show that even with our relatively simple techniques it is possible to verify systems that are known to be hard for BDD-based model checkers.
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Symbolic Reachability Analysis based on SAT Solvers
2000Co-Authors: Parosh Aziz Abdulla, Per Bjesse, Niklas EénAbstract:. The introduction of symbolic model checking using Binary Decision Diagrams (BDDs) has led to a substantial extension of the class of systems which can be algorithmically verified. Although BDDs have played a crucial role in this success they have some well-known drawbacks, such as requiring an externally supplied variable ordering and causing space blowups in certain applications. In a parallel development, SAT solving Procedures, such as Stalmarck's method or the Davis-Putnam Procedure, have been used successfully in verifying very large industrial systems. These efforts have recently attracted the attention of the model checking community resulting in the notion of bounded model checking. In this paper, we show how to adapt standard algorithms for symbolic reachability analysis to work with SAT-solvers. The key element of our contribution is the combination of an algorithm that removes quantifiers over propositional variables and a simple representation that allows re..
