Abstract
Complete algorithms for constraint solving typically exploit properties like (in)consistency or interchangeability, which they detect by means of incomplete yet effective algorithms and use to reduce the search space. In this paper, we study a wide range of properties which includes most of the ones used by existing CSP algorithms as well as some which have not yet been considered in the literature, and we investigate their use in CSP solving. We clarify the relationships between these notions and characterise the complexity of the problem of checking them. Following the CSP approach, we then determine a number of relaxations (for instance local versions) which provide sufficient conditions whose detection is tractable. This work is a first step towards a comprehensive framework for CSP properties, and it also shows that new notions still remain to be exploited.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Cadoli, M., Mancini, T.: Exploiting functional dependencies in declarative problem specifications. In: Alferes, J.J., Leite, J. (eds.) JELIA 2004. LNCS (LNAI), vol. 3229, pp. 628–640. Springer, Heidelberg (2004)
Cadoli, M., Mancini, T.: Using a theorem prover for reasoning on constraint problems. In: 3rd Int. CP Workshop on Modelling and Reformulating CSPs (2004)
Choueiry, B., Lal, A., Freuder, E.C.: Interchangeability and dynamic bundling for non-binary finite CSPs. In: Int. Workshop on Constraint Solving and Constraint Logic Programming (CSCLP), Springer, Heidelberg (2004) (page to appear)
Choueiry, B., Noubir, G.: On the computation of local interchangeability in discrete constraint satisfaction problems. In: Nat (US) Conf. on Artificial Intelligence (AAAI), pp. 326–333. AAAI, Menlo Park (1998)
Crawford, J.M.: A theoretical analysis of reasoning by symmetry in first-order logic (extended abstract). In: AAAI Workshop on Tractable Reasoning (1992)
Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Int. Conf. on Principles of Knowledge Representation and Reasoning (KR), pp. 148–159. Morgan Kaufmann, San Francisco (1996)
Davis, M., Putnam, H.: A computing procedure for quantification theory. J. of the ACM 7(3), 201–215 (1960)
Dechter, R.: Constraint networks (survey). In: Encyclopedia of Artificial Intelligence, 2nd edn., pp. 276–285 (1992)
Even, S., Selman, A., Yacobi, Y.: The complexity of promise problems with applications to public-key cryptography. Information and Control 61(2), 159–173 (1984)
Freuder, E.C.: Synthesizing constraint expressions. Comm. of the ACM 21(11), 958–966 (1978)
Freuder, E.C.: Eliminating interchangeable values in constraint satisfaction problems. In: Nat (US) Conf. on Artificial Intelligence (AAAI), pp. 227–233. AAAI Press, Menlo Park (1991)
Gent, I.P., Smith, B.M.: Symmetry breaking in constraint programming. In: Euro. Conf. on Artificial Intelligence (ECAI), pp. 599–603. IOS Press, Amsterdam (2000)
Giunchiglia, E., Massarotto, A., Sebastiani, R.: Act, and the rest will follow: Exploiting determinism in planning as satisfiability. In: Nat (US) Conf. on Artificial Intelligence (AAAI), pp. 948–953. AAAI Press, Menlo Park (1998)
Jeavons, P., Cohen, D.A., Cooper, M.C.: A substitution operation for constraints. In: Int. Conf. on Principles and Practice of Constraint Programming (CP), pp. 1–9. Springer, Heidelberg (1994)
Jonsson, P., Krokhin, A.: Recognizing frozen variables in constraint satisfaction problems. Theoretical Computer Science (TCS) 329(1-3), 93–113 (2004)
Köbler, J., Schöning, U., Torán, J.: The graph isomorphism problem: its computational complexitypp. Birkhäuser, Basel (1993)
Lenstra, A., Lenstra, H.W.: Algorithms in number theory. In: van Leeuwen, J. (ed.) The Handbook of Theoretical Computer Science. Algorithms and Complexity, vol. 1, MIT Press, Cambridge (1990)
Li, C.M.: Integrating equivalency reasoning into Davis-Putnam procedure. In: Nat (US) Conf. on Artificial Intelligence (AAAI), pp. 291–296. AAAI press, Menlo Park (2000)
Mackworth, A.K.: Consistency in networks of relations. Artificial Intelligence 8, 99–118 (1977)
Monasson, R., Zecchina, R., Kirkpatrick, S., Selman, B., Troyansky, L.: Determining computational complexity from characteristic ‘phase transitions’. Nature 400, 133–137 (1999)
Montanari, U.: Networks of constraints: Fundamental properties and applications to picture processing. Information Science 7(2), 85–132 (1974)
Papadimitriou, C.H.: Computational Complexity. Addison-Wesley, Reading (1994)
Pyhälä, T.: Factoring benchmarks for SAT solvers. Technical report, Helsinki university of technology (2004)
Schaefer, T.J.: The complexity of satisfiability problems. In: ACM Symp. on Theory of Computing (STOC), pp. 216–226. ACM, New York (1978)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bordeaux, L., Cadoli, M., Mancini, T. (2005). Exploiting Fixable, Removable, and Implied Values in Constraint Satisfaction Problems. In: Baader, F., Voronkov, A. (eds) Logic for Programming, Artificial Intelligence, and Reasoning. LPAR 2005. Lecture Notes in Computer Science(), vol 3452. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-32275-7_19
Download citation
DOI: https://doi.org/10.1007/978-3-540-32275-7_19
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-25236-8
Online ISBN: 978-3-540-32275-7
eBook Packages: Computer ScienceComputer Science (R0)