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Torsten Schaub - One of the best experts on this subject based on the ideXlab platform.
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LION - Robust Benchmark Set Selection for Boolean Constraint Solvers
Lecture Notes in Computer Science, 2013Co-Authors: Holger H Hoos, Torsten Schaub, Benjamin Kaufmann, Marius SchneiderAbstract:We investigate the composition of representative benchmark sets for evaluating and improving the performance of robust Boolean Constraint solvers in the context of satisfiability testing and answer set programming. Starting from an analysis of current practice, we isolate a set of desiderata for guiding the development of a parametrized benchmark selection algorithm. Our algorithm samples a benchmark set from a larger base set or distribution comprising a large variety of instances. This is done fully automatically, in a way that carefully calibrates instance hardness and instance similarity. We demonstrate the usefulness of this approach by means of empirical results showing that optimizing solvers on the benchmark sets produced by our method leads to better configurations than obtained based on the much larger, original sets.
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robust benchmark set selection for Boolean Constraint solvers
Learning and Intelligent Optimization, 2013Co-Authors: Holger H Hoos, Torsten Schaub, Benjamin Kaufmann, Marius SchneiderAbstract:We investigate the composition of representative benchmark sets for evaluating and improving the performance of robust Boolean Constraint solvers in the context of satisfiability testing and answer set programming. Starting from an analysis of current practice, we isolate a set of desiderata for guiding the development of a parametrized benchmark selection algorithm. Our algorithm samples a benchmark set from a larger base set or distribution comprising a large variety of instances. This is done fully automatically, in a way that carefully calibrates instance hardness and instance similarity. We demonstrate the usefulness of this approach by means of empirical results showing that optimizing solvers on the benchmark sets produced by our method leads to better configurations than obtained based on the much larger, original sets.
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CP - Answer Set Programming: Boolean Constraint Solving for Knowledge Representation and Reasoning
Lecture Notes in Computer Science, 2013Co-Authors: Torsten SchaubAbstract:Answer Set Programming ASP; [1,2,3] is a declarative problem solving approach, combining a rich yet simple modeling language with high-performance Boolean Constraint solving capacities. ASP is particularly suited for modeling problems in the area of Knowledge Representation and Reasoning involving incomplete, inconsistent, and changing information. As such, it offers, in addition to satisfiability testing, various reasoning modes, including different forms of model enumeration, intersection or unioning, as well as multi-criteria and -objective optimization. From a formal perspective, ASP allows for solving all search problems in NP and NP NP in a uniform way. Hence, ASP is wellsuited for solving hard combinatorial search problems, like system design and timetabling. Prestigious applications of ASP include composition of Renaissance music [4], decision support systems for NASA shuttle controllers [5], reasoning tools in systems biology [6,7,8] and robotics [9,10], industrial team-building [11], and many more. The versatility of ASP is nicely reflected by the ASP solver clasp [12], winning first places at various solver competitions, such as ASP,MISC, PB, and SAT competitions. The solver clasp is at the heart of the open source platform Potassco hosted at potassco.sourceforge.net . Potassco stands for the "Potsdam Answer Set Solving Collection" [13] and has seen more than 30000 downloads world-wide since its inception at the end of 2008. The talk will start with an introduction to ASP, its modeling language and solving methodology, and portray some distinguished ASP systems.
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CPAIOR - Solution Enumeration for Projected Boolean Search Problems
Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems, 2009Co-Authors: Martin Gebser, Benjamin Kaufmann, Torsten SchaubAbstract:Many real-world problems require the enumeration of all solutions of combinatorial search problems, even though this is often infeasible in practice. However, not always all parts of a solution are needed. We are thus interested in projecting solutions to a restricted vocabulary. Yet, the adaption of Boolean Constraint solving algorithms turns out to be non-obvious provided one wants a repetition-free enumeration in polynomial space. We address this problem and propose a new algorithm computing projective solutions. Although we have implemented our approach in the context of Answer Set Programming, it is readily applicable to any solver based on modern Boolean Constraint technology.
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KR - Conflict-driven disjunctive answer set solving
2008Co-Authors: Christian Drescher, Benjamin Kaufmann, Martin Gebser, Torsten Grote, Arne König, Max Ostrowski, Torsten SchaubAbstract:We elaborate a uniform approach to computing answer sets of disjunctive logic programs based on state-of-the-art Boolean Constraint solving techniques. Starting from a Constraint-based characterization of answer sets, we develop advanced solving algorithms, featuring backjumping and conflict-driven learning using the First-UIP scheme as well as sophisticated unfounded set checking. As a final result, we obtain a competitive solver for ΣP2-complete problems, taking advantage of Boolean Constraint solving technology without using any legacy solvers as black boxes.
Heribert Vollmer - One of the best experts on this subject based on the ideXlab platform.
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Boolean Constraint satisfaction problems when does post s lattice help
Complexity of Constraints, 2008Co-Authors: Nadia Creignou, Heribert VollmerAbstract:The propositional satisfiability problem SAT, i.e., the problemto decide, given a propositional formula φ (without loss ofgenerality in conjunctive normal form CNF), if there is anassignment to the variables in φ that satisfies φ, is thehistorically first and standard NP-complete problem [Coo71].However, there are well-known syntactic restrictions for whichsatisfiability is efficiently decidable, for example if everyclause in the CNF formula has at most two literals (2CNF formulas)or if every clause has at most one positive literal (Horn formulas)or at most one negative literal (dual Horn formulas), see [KL99].To study this phenomenon more generally, we study formulas with“clauses” of arbitrary shapes, i.e., consisting ofapplying arbitrary relations R ⊆ {0,1} k to (notnecessarily distinct) variables x 1,...,x k . A Constraint languageΓ is a finite set of such relations. In the rest of thischapter, Γ and Γ′ will always denote BooleanConstraint languages. A Γ-formula is a conjunction of clausesR(x 1,...,x k ) as above using only relations R from Γ. Thefor us central family of algorithmic problems, parameterized by aConstraint language Γ, now is the problem to determinesatisfiability of a given Γ-formula, denoted byCsp(Γ).
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Complexity of Constraints - Boolean Constraint Satisfaction Problems: When Does Post's Lattice Help?
Complexity of Constraints, 2008Co-Authors: Nadia Creignou, Heribert VollmerAbstract:The propositional satisfiability problem SAT, i.e., the problemto decide, given a propositional formula φ (without loss ofgenerality in conjunctive normal form CNF), if there is anassignment to the variables in φ that satisfies φ, is thehistorically first and standard NP-complete problem [Coo71].However, there are well-known syntactic restrictions for whichsatisfiability is efficiently decidable, for example if everyclause in the CNF formula has at most two literals (2CNF formulas)or if every clause has at most one positive literal (Horn formulas)or at most one negative literal (dual Horn formulas), see [KL99].To study this phenomenon more generally, we study formulas with“clauses” of arbitrary shapes, i.e., consisting ofapplying arbitrary relations R ⊆ {0,1} k to (notnecessarily distinct) variables x 1,...,x k . A Constraint languageΓ is a finite set of such relations. In the rest of thischapter, Γ and Γ′ will always denote BooleanConstraint languages. A Γ-formula is a conjunction of clausesR(x 1,...,x k ) as above using only relations R from Γ. Thefor us central family of algorithmic problems, parameterized by aConstraint language Γ, now is the problem to determinesatisfiability of a given Γ-formula, denoted byCsp(Γ).
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computational complexity of Constraint satisfaction
Conference on Computability in Europe, 2007Co-Authors: Heribert VollmerAbstract:The input to a Constraint satisfaction problem (CSP) consists of a set of variables, each with a domain, and Constraints between these variables formulated by relations over the appropriate domains; the question is if there is an assignment of values to the variables that satisfies all Constraints. Different algorithmic tasks for CSPs (checking satisfiability, counting the number of solutions, enumerating all solutions) can be used to model many problems in areas such as computational logic, artificial intelligence, circuit design, etc. We will survey results on the complexity of these computational tasks as a function of properties of the allowed Constraint relations. Particular attention is paid to the special case of Boolean Constraint relations.
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Bases for Boolean co-clones
Information Processing Letters, 2005Co-Authors: Elmar Böhler, Steffen Reith, Henning Schnoor, Heribert VollmerAbstract:The complexity of various problems in connection with Boolean Constraints, like, for example, quantified Boolean Constraint satisfaction, have been studied recently. Depending on what types of Constraints may be used, the complexity of such problems varies. A very interesting observation of the recent past has been that the thus derived classification of Constraints can be explained with the help of universal algebra. More precisely, the difficulty of such a Constraint problem often depends on the co-clone the Constraints are from. A co-clone is a set of Boolean relations that is closed under very natural closure operations. Nearly all these co-clones can be generated by said operators out of a finite set of relations, a so-called base. Knowing a, preferably simple, base for each co-clone can therefore be of great value when studying the complexity of Boolean Constraint problems, since this knowledge reduces the infinitely many cases of equivalent problems to a single one--the Constraint satisfaction problem for this base. In this paper we give a finite and simple base for every Boolean co-clone, where this is possible. We give evidence that the presented bases are as easy as possible.
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The complexity of Boolean Constraint isomorphism
Lecture Notes in Computer Science, 2004Co-Authors: Elmar Böhler, Edith Hemaspaandra, Steffen Reith, Heribert VollmerAbstract:We consider the Boolean Constraint isomorphism problem, that is, the problem of determining whether two sets of Boolean Constraint applications can be made equivalent by renaming the variables. We show that depending on the set of allowed Constraints, the problem is either coNP-hard and GI-hard, equivalent to graph isomorphism, or polynomial-time solvable. This establishes a complete classification of the complexity of the problem, and moreover, it identifies exactly all those cases in which Boolean Constraint isomorphism is polynomial-time many-one equivalent to graph isomorphism, the best-known and best-examined isomorphism problem in theoretical computer science.
Marius Schneider - One of the best experts on this subject based on the ideXlab platform.
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LION - Robust Benchmark Set Selection for Boolean Constraint Solvers
Lecture Notes in Computer Science, 2013Co-Authors: Holger H Hoos, Torsten Schaub, Benjamin Kaufmann, Marius SchneiderAbstract:We investigate the composition of representative benchmark sets for evaluating and improving the performance of robust Boolean Constraint solvers in the context of satisfiability testing and answer set programming. Starting from an analysis of current practice, we isolate a set of desiderata for guiding the development of a parametrized benchmark selection algorithm. Our algorithm samples a benchmark set from a larger base set or distribution comprising a large variety of instances. This is done fully automatically, in a way that carefully calibrates instance hardness and instance similarity. We demonstrate the usefulness of this approach by means of empirical results showing that optimizing solvers on the benchmark sets produced by our method leads to better configurations than obtained based on the much larger, original sets.
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robust benchmark set selection for Boolean Constraint solvers
Learning and Intelligent Optimization, 2013Co-Authors: Holger H Hoos, Torsten Schaub, Benjamin Kaufmann, Marius SchneiderAbstract:We investigate the composition of representative benchmark sets for evaluating and improving the performance of robust Boolean Constraint solvers in the context of satisfiability testing and answer set programming. Starting from an analysis of current practice, we isolate a set of desiderata for guiding the development of a parametrized benchmark selection algorithm. Our algorithm samples a benchmark set from a larger base set or distribution comprising a large variety of instances. This is done fully automatically, in a way that carefully calibrates instance hardness and instance similarity. We demonstrate the usefulness of this approach by means of empirical results showing that optimizing solvers on the benchmark sets produced by our method leads to better configurations than obtained based on the much larger, original sets.
Michel Rueher - One of the best experts on this subject based on the ideXlab platform.
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Exploration of the capabilities of Constraint programming for software verification
Lecture Notes in Computer Science, 2006Co-Authors: Hélène Collavizza, Michel RueherAbstract:Verification and validation are two of the most critical issues in the software engineering process. Numerous techniques ranging from formal proofs to testing methods have been used during the last years to verify the conformity of a program with its specification. Recently, Constraint programming techniques have been used to generate test data. In this paper we investigate the capabilities of Constraint programming techniques to verify the conformity of a program with its specification. We introduce here a new approach based on a transformation of both the program and its specification in a Constraint system. To establish the conformity we demonstrate that the union of the Constraint system derived from the program and the negation of the Constraint system derived from its specification is inconsistent (for the considered domains of values). This verification process consists of three steps. First, we generate a Boolean Constraint system which captures the information provided by the control flow graph. Then, we use a SAT solver to solve the Boolean Constraint system. Finally, for each Boolean solution we build a new Constraint system over finite domains and solve it. The latter system captures the operational part of the program and the specification. Boolean Constraints play an essential role since they drastically reduce the search space before the search and enumeration processes start. Moreover, in the case where the program is not conforming with its specification, Boolean Constraints provide a powerful tool for finding wrong behaviours in different execution paths of the program. First experimental results on standard benchmarks are very promising.
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TACAS - Exploration of the capabilities of Constraint programming for software verification
Tools and Algorithms for the Construction and Analysis of Systems, 2006Co-Authors: Hélène Collavizza, Michel RueherAbstract:Verification and validation are two of the most critical issues in the software engineering process. Numerous techniques ranging from formal proofs to testing methods have been used during the last years to verify the conformity of a program with its specification. Recently, Constraint programming techniques have been used to generate test data. In this paper we investigate the capabilities of Constraint programming techniques to verify the conformity of a program with its specification. We introduce here a new approach based on a transformation of both the program and its specification in a Constraint system. To establish the conformity we demonstrate that the union of the Constraint system derived from the program and the negation of the Constraint system derived from its specification is inconsistent (for the considered domains of values). This verification process consists of three steps. First, we generate a Boolean Constraint system which captures the information provided by the control flow graph. Then, we use a SAT solver to solve the Boolean Constraint system. Finally, for each Boolean solution we build a new Constraint system over finite domains and solve it. The latter system captures the operational part of the program and the specification. Boolean Constraints play an essential role since they drastically reduce the search space before the search and enumeration processes start. Moreover, in the case where the program is not conforming with its specification, Boolean Constraints provide a powerful tool for finding wrong behaviours in different execution paths of the program. First experimental results on standard benchmarks are very promising.
Holger H Hoos - One of the best experts on this subject based on the ideXlab platform.
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LION - Robust Benchmark Set Selection for Boolean Constraint Solvers
Lecture Notes in Computer Science, 2013Co-Authors: Holger H Hoos, Torsten Schaub, Benjamin Kaufmann, Marius SchneiderAbstract:We investigate the composition of representative benchmark sets for evaluating and improving the performance of robust Boolean Constraint solvers in the context of satisfiability testing and answer set programming. Starting from an analysis of current practice, we isolate a set of desiderata for guiding the development of a parametrized benchmark selection algorithm. Our algorithm samples a benchmark set from a larger base set or distribution comprising a large variety of instances. This is done fully automatically, in a way that carefully calibrates instance hardness and instance similarity. We demonstrate the usefulness of this approach by means of empirical results showing that optimizing solvers on the benchmark sets produced by our method leads to better configurations than obtained based on the much larger, original sets.
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robust benchmark set selection for Boolean Constraint solvers
Learning and Intelligent Optimization, 2013Co-Authors: Holger H Hoos, Torsten Schaub, Benjamin Kaufmann, Marius SchneiderAbstract:We investigate the composition of representative benchmark sets for evaluating and improving the performance of robust Boolean Constraint solvers in the context of satisfiability testing and answer set programming. Starting from an analysis of current practice, we isolate a set of desiderata for guiding the development of a parametrized benchmark selection algorithm. Our algorithm samples a benchmark set from a larger base set or distribution comprising a large variety of instances. This is done fully automatically, in a way that carefully calibrates instance hardness and instance similarity. We demonstrate the usefulness of this approach by means of empirical results showing that optimizing solvers on the benchmark sets produced by our method leads to better configurations than obtained based on the much larger, original sets.