On finite Taylor algebras

2016 ◽  
Vol 26 (08) ◽  
pp. 1547-1571
Author(s):  
Alexander Wires
Keyword(s):  
Constraint Satisfaction ◽  
Constraint Satisfaction Problems ◽  
Algebraic Constructions ◽  
Bounded Width

We establish a new hereditary characterization of finite idempotent Taylor algebras. This generalizes the algebraic constructions which figured in the recent successful characterization of the correctness of the bounded width algorithm for constraint satisfaction problems by finite idempotent algebras generating congruence meet-semidistributive varieties. We introduce the cyclic reduct of a finite Taylor algebra and prove a collapse of Mal’cev conditions.

scholarly journals Constraint programming viewed as rule-based programming

2001 ◽  
Vol 1 (6) ◽  
pp. 713-750 ◽  
Author(s):  
KRZYSZTOF R. APT ◽  
ERIC MONFROY
Keyword(s):  
Constraint Satisfaction ◽  
Constraint Programming ◽  
Constraint Satisfaction Problems ◽  
Rule Based ◽  
Local Consistency ◽  
Arc Consistency ◽  
Computation Process ◽  
Rule Based Approach ◽  
Rule Consistency

We study here a natural situation when constraint programming can be entirely reduced to rule-based programming. To this end we explain first how one can compute on constraint satisfaction problems using rules represented by simple first-order formulas. Then we consider constraint satisfaction problems that are based on predefined, explicitly given constraints. To solve them we first derive rules from these explicitly given constraints and limit the computation process to a repeated application of these rules, combined with labeling. We consider two types of rule here. The first type, that we call equality rules, leads to a new notion of local consistency, called rule consistency that turns out to be weaker than arc consistency for constraints of arbitrary arity (called hyper-arc consistency in Marriott & Stuckey (1998)). For Boolean constraints rule consistency coincides with the closure under the well-known propagation rules for Boolean constraints. The second type of rules, that we call membership rules, yields a rule-based characterization of arc consistency. To show feasibility of this rule-based approach to constraint programming, we show how both types of rules can be automatically generated, as CHR rules of Frühwirth (1995). This yields an implementation of this approach to programming by means of constraint logic programming. We illustrate the usefulness of this approach to constraint programming by discussing various examples, including Boolean constraints, two typical examples of many valued logics, constraints dealing with Waltz's language for describing polyhedral scenes, and Allen's qualitative approach to temporal logic.

scholarly journals Semantic Width and the Fixed-Parameter Tractability of Constraint Satisfaction Problems

2020 ◽  
Author(s):  
Hubie Chen ◽  
Georg Gottlob ◽  
Matthias Lanzinger ◽  
Reinhard Pichler
Keyword(s):  
Constraint Satisfaction ◽  
Fundamental Problem ◽  
Constraint Satisfaction Problems ◽  
Fixed Parameter Tractability ◽  
Scheduling Problems ◽  
Fixed Parameter Tractable ◽  
Database Theory ◽  
Formal Framework ◽  
Fixed Parameter

Constraint satisfaction problems (CSPs) are an important formal framework for the uniform treatment of various prominent AI tasks, e.g., coloring or scheduling problems. Solving CSPs is, in general, known to be NP-complete and fixed-parameter intractable when parameterized by their constraint scopes. We give a characterization of those classes of CSPs for which the problem becomes fixed-parameter tractable. Our characterization significantly increases the utility of the CSP framework by making it possible to decide the fixed-parameter tractability of problems via their CSP formulations. We further extend our characterization to the evaluation of unions of conjunctive queries, a fundamental problem in databases. Furthermore, we provide some new insight on the frontier of PTIME solvability of CSPs. In particular, we observe that bounded fractional hypertree width is more general than bounded hypertree width only for classes that exhibit a certain type of exponential growth. The presented work resolves a long-standing open problem and yields powerful new tools for complexity research in AI and database theory.

scholarly journals Truth-Preservation under Fuzzy pp-Formulas

2019 ◽  
Vol 27 (Supp01) ◽  
pp. 89-105
Author(s):  
Pilar Dellunde ◽  
Amanda Vidal
Keyword(s):  
Computer Science ◽  
Constraint Satisfaction ◽  
Classical Logic ◽  
Constraint Satisfaction Problems ◽  
Algebraic Characterization ◽  
Theoretic Approach ◽  
Direct Products ◽  
Fuzzy Constraint ◽  
Fuzzy Constraint Satisfaction

How can non-classical logic contribute to the analysis of complexity in computer science? In this paper, we give a step towards this question, taking a logical model-theoretic approach to the analysis of complexity in fuzzy constraint satisfaction. We study fuzzy positive-primitive sentences, and we present an algebraic characterization of classes axiomatized by this kind of sentences in terms of homomorphisms and direct products. The ultimate goal is to study the expressiveness and reasoning mechanisms of non-classical languages, with respect to constraint satisfaction problems and, in general, in modelling decision scenarios.

scholarly journals Finding robust solutions for constraint satisfaction problems with discrete and ordered domains by coverings

2013 ◽  
Vol 44 (2) ◽  
pp. 131-156 ◽  
Author(s):  
Laura Climent ◽  
Richard J. Wallace ◽  
Miguel A. Salido ◽  
Federico Barber
Keyword(s):  
Constraint Satisfaction ◽  
Constraint Satisfaction Problems ◽  
Robust Solutions

scholarly journals A fine-grained arc-consistency algorithm for non-normalized constraint satisfaction problems

2011 ◽  
Vol 21 (4) ◽  
pp. 733-744 ◽  
Author(s):  
Marlene Arangú ◽  
Miguel Salido
Keyword(s):  
Constraint Satisfaction ◽  
Constraint Programming ◽  
Real Life ◽  
Search Space ◽  
Constraint Satisfaction Problems ◽  
Fine Grained ◽  
Arc Consistency ◽  
Life Problems ◽  
Programming Techniques ◽  
Np Complete

A fine-grained arc-consistency algorithm for non-normalized constraint satisfaction problems Constraint programming is a powerful software technology for solving numerous real-life problems. Many of these problems can be modeled as Constraint Satisfaction Problems (CSPs) and solved using constraint programming techniques. However, solving a CSP is NP-complete so filtering techniques to reduce the search space are still necessary. Arc-consistency algorithms are widely used to prune the search space. The concept of arc-consistency is bidirectional, i.e., it must be ensured in both directions of the constraint (direct and inverse constraints). Two of the most well-known and frequently used arc-consistency algorithms for filtering CSPs are AC3 and AC4. These algorithms repeatedly carry out revisions and require support checks for identifying and deleting all unsupported values from the domains. Nevertheless, many revisions are ineffective, i.e., they cannot delete any value and consume a lot of checks and time. In this paper, we present AC4-OP, an optimized version of AC4 that manages the binary and non-normalized constraints in only one direction, storing the inverse founded supports for their later evaluation. Thus, it reduces the propagation phase avoiding unnecessary or ineffective checking. The use of AC4-OP reduces the number of constraint checks by 50% while pruning the same search space as AC4. The evaluation section shows the improvement of AC4-OP over AC4, AC6 and AC7 in random and non-normalized instances.

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