Semiring-Based CSPs and Valued CSPs: Basic Properties and Comparison

In this paper we describe two frameworks for constraint solving where classical CSPs, fuzzy CSPs, weighted CSPs, partial constraint satisfaction, and others can be easily cast. One is based on a semiring, and the other one on a totally ordered commutative monoid. We then compare the two approaches and we discuss the relationship between them. The two frameworks have been independently introduced in [2] and [28].

[1]  Eugene C. Freuder.  Backtrack-free and backtrack-bounded search , 1988 .

[2]  Ugo Montanari,et al.  Networks of constraints: Fundamental properties and applications to picture processing , 1974, Inf. Sci..

[3]  L. Zadeh.  Calculus of fuzzy restrictions , 1996 .

[4]  Francesca Rossi,et al.  Constraint Relaxation may be Perfect , 1991, Artif. Intell..

[5]  Z. Ruttkay.  Fuzzy constraint satisfaction , 1994, Proceedings of 1994 IEEE 3rd International Fuzzy Systems Conference.

[6]  D. Dubois,et al.  The calculus of fuzzy restrictions as a basis for flexible constraint satisfaction , 1993, [Proceedings 1993] Second IEEE International Conference on Fuzzy Systems.

[7]  Francesca Rossi,et al.  Constraint Solving over Semirings , 1995, IJCAI.

[8]  Thomas Schiex,et al.  Possibilistic Constraint Satisfaction Problems or "How to Handle Soft Constraints?" , 1992, UAI.

[9]  Thomas Schiex,et al.  Valued Constraint Satisfaction Problems: Hard and Easy Problems , 1995, IJCAI.

[10]  Eugene C. Freuder,et al.  An Efficient Cross Product Representation of the Constraint Satisfaction Problem Search Space , 1992, AAAI.

[11]  Richard J. Wallace,et al.  Partial Constraint Satisfaction , 1989, IJCAI.

[12]  H. Moulin.  Axioms of Cooperative Decision Making , 1988 .

[13]  Azriel Rosenfeld,et al.  Scene Labeling by Relaxation Operations , 1976, IEEE Transactions on Systems, Man, and Cybernetics.

[14]  Eugene C. Freuder,et al.  The Complexity of Some Polynomial Network Consistency Algorithms for Constraint Satisfaction Problems , 1985, Artif. Intell..

[15]  David S. Johnson,et al.  Some Simplified NP-Complete Graph Problems , 1976, Theor. Comput. Sci..

[16]  Robert M. Haralick,et al.  Structural Descriptions and Inexact Matching , 1981, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[17]  Jf Baldwin,et al.  Encyclopedia of AI , 1992 .

[18]  Mark W. Krentel.  The complexity of optimization problems , 1986, STOC '86.

[19]  Eugene C. Freuder.  Synthesizing constraint expressions , 1978, CACM.

[20]  Alan K. Mackworth.  Consistency in Networks of Relations , 1977, Artif. Intell..

[21]  Constantin V. Negoita,et al.  On Fuzzy Systems , 1978 .

[22]  Michael J. Maher,et al.  Constraint Hierarchies and Logic Programming , 1989, ICLP.

[23]  T. Pavlidis,et al.  Fuzzy sets and their applications to cognitive and decision processes , 1977 .

[24]  Vipin Kumar,et al.  Algorithms for Constraint-Satisfaction Problems: A Survey , 1992, AI Mag..

[25]  Jérôme Lang,et al.  Uncertainty in Constraint Satisfaction Problems: a Probalistic Approach , 1993, ECSQARU.

[26]  Didier Dubois,et al.  A class of fuzzy measures based on triangular norms , 1982 .

[27]  Joxan Jaffar,et al.  Constraint logic programming , 1987, POPL '87.

[28]  Thomas Schiex,et al.  Selecting preferred solutions in Fuzzy Constraint Satisfaction Problems , 1993 .

[29]  Eugene C. Freuder,et al.  Improved relaxation and search methods for approximate constraint satisfaction with a maximin criter , 1990 .

[30]  Nicolas Beldiceanu,et al.  Constraint Logic Programming , 1997 .