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72
SEM: A System for Enumerating Models
 Department of Philosophy University of WisconsinMadison Mathematics and Computer Science
, 1995
"... Model generation can be regarded as a special case of the Constraint Satisfaction Problem (CSP). It has many applications in AI, computer science and mathematics. In this paper, we describe SEM, a System for Enumerating finite Models of firstorder manysorted theories. To the best of our knowledge, ..."
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Cited by 70 (2 self)
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Model generation can be regarded as a special case of the Constraint Satisfaction Problem (CSP). It has many applications in AI, computer science and mathematics. In this paper, we describe SEM, a System for Enumerating finite Models of firstorder manysorted theories. To the best of our knowledge, SEM outperforms any other finite model generation system on many test problems. The high performance of SEM relies on the following two techniques: (a) an efficient implementation of constraint propagation which requires little dynamic allocation of storage; (b) a powerful heuristic which eliminates many isomorphic partial models during the search. We will present the basic algorithm of SEM along with these two techniques. Our experimental results show that general purpose finite model generators are indeed useful in many applications. 1
PSATO: a Distributed Propositional Prover and Its Application to Quasigroup Problems
 Journal of Symbolic Computation
, 1996
"... This paper shows a way of using such resources to solve hard problems. ..."
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Cited by 68 (4 self)
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This paper shows a way of using such resources to solve hard problems.
On the Notion of Interestingness in Automated Mathematical Discovery
 International Journal of Human Computer Studies
, 2000
"... We survey ve mathematical discovery programs by looking in detail at the discovery processes they illustrate and the success they've had. We focus on how they estimate the interestingness of concepts and conjectures and extract some common notions about interestingness in automated mathematical ..."
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Cited by 64 (25 self)
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We survey ve mathematical discovery programs by looking in detail at the discovery processes they illustrate and the success they've had. We focus on how they estimate the interestingness of concepts and conjectures and extract some common notions about interestingness in automated mathematical discovery. We detail how empirical evidence is used to give plausibility to conjectures, and the dierent ways in which a result can be thought of as novel. We also look at the ways in which the programs assess how surprising and complex a conjecture statement is, and the dierent ways in which the applicability of a concept or conjecture is used. Finally, we note how a user can set tasks for the program to achieve and how this aects the calculation of interestingness. We conclude with some hints on the use of interestingness measures for future developers of discovery programs in mathematics.
Kodkod: A relational model finder
 In Tools and Algorithms for Construction and Analysis of Systems (TACAS
, 2007
"... Abstract. The key design challenges in the construction of a SATbased relational model finder are described, and novel techniques are proposed to address them. An efficient model finder must have a mechanism for specifying partial solutions, an effective symmetry detection and breaking scheme, and ..."
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Cited by 60 (4 self)
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Abstract. The key design challenges in the construction of a SATbased relational model finder are described, and novel techniques are proposed to address them. An efficient model finder must have a mechanism for specifying partial solutions, an effective symmetry detection and breaking scheme, and an economical translation from relational to boolean logic. These desiderata are addressed with three new techniques: a symmetry detection algorithm that works in the presence of partial solutions, a sparsematrix representation of relations, and a compact representation of boolean formulas inspired by boolean expression diagrams and reduced boolean circuits. The presented techniques have been implemented and evaluated, with promising results. 1
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.
Otter: The CADE13 Competition Incarnations
 JOURNAL OF AUTOMATED REASONING
, 1997
"... This article discusses the two incarnations of Otter entered in the CADE13 Automated Theorem Proving Competition. Also presented are some historical background, a summary of applications that have led to new results in mathematics and logic, and a general discussion of Otter. ..."
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Cited by 43 (3 self)
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This article discusses the two incarnations of Otter entered in the CADE13 Automated Theorem Proving Competition. Also presented are some historical background, a summary of applications that have led to new results in mathematics and logic, and a general discussion of Otter.
NORA/HAMMR: Making DeductionBased Software Component Retrieval Practical
, 1997
"... Deductionbased software component retrieval uses preand postconditions as indexes and search keys and an automated theorem prover (ATP) to check whether a component matches. This idea is very simple but the vast number of arising proof tasks makes a practical implementation very hard. We thus pass ..."
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Cited by 39 (4 self)
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Deductionbased software component retrieval uses preand postconditions as indexes and search keys and an automated theorem prover (ATP) to check whether a component matches. This idea is very simple but the vast number of arising proof tasks makes a practical implementation very hard. We thus pass the components through a chain of filters of increasing deductive power. In this chain, rejection filters based on signature matching and model checking techniques are used to rule out nonmatches as early as possible and to prevent the subsequent ATP from "drowning." Hence, intermediate results of reasonable precision are available at (almost) any time of the retrieval process. The final ATP step then works as a confirmation filter to lift the precision of the answer set. We implemented a chain which runs fully automatically and uses MACE for model checking and the automated prover SETHEO as confirmation filter. We evaluated the system over a mediumsized collection of components. The resul...
Automatic Concept Formation in Pure Mathematics
"... The HR program forms concepts and makes conjectures in domains of pure mathematics andusestheoremproverOTTERandmodel generatorMACEtoproveordisprovetheconjectures. HRmeasurespropertiesofconcepts andassessesthetheoremsandproofsinvolving themtoestimatetheinterestingnessofeach concept and employ a best ..."
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Cited by 38 (28 self)
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The HR program forms concepts and makes conjectures in domains of pure mathematics andusestheoremproverOTTERandmodel generatorMACEtoproveordisprovetheconjectures. HRmeasurespropertiesofconcepts andassessesthetheoremsandproofsinvolving themtoestimatetheinterestingnessofeach concept and employ a best first search. This approachhasledHRtothediscoveryofinterestingnewmathematics and enables it to build theories from just the axioms of finite algebras.
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.
Creativity versus the perception of creativity in computational systems
 In Proceedings of the AAAI Spring Symp. on Creative Intelligent Systems
, 2008
"... We add to the discussion of how to assess the creativity of programs which generate artefacts such as poems, theorems, paintings, melodies, etc. To do so, we first review some existing frameworks for assessing artefact generation programs. Then, drawing on our experience of building both a mathemati ..."
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Cited by 32 (10 self)
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We add to the discussion of how to assess the creativity of programs which generate artefacts such as poems, theorems, paintings, melodies, etc. To do so, we first review some existing frameworks for assessing artefact generation programs. Then, drawing on our experience of building both a mathematical discovery system and an automated painter, we argue that it is not appropriate to base the assessment of a system on its output alone, and that the way it produces artefacts also needs to be taken into account. We suggest a simple framework within which the behaviour of a program can be categorised and described which may add to the perception of creativity in the system.