Collapsibility in Infinite-Domain Quantified Constraint Satisfaction

In this article, we study the quantified constraint satisfaction problem (QCSP) over infinite domains. We develop a technique called collapsibility that allows one to give strong complexity upper bounds on the QCSP. This technique makes use of both logical and universal-algebraic ideas. We give applications illustrating the use of our technique.

[1]  Víctor Dalmau,et al.  Generalized majority-minority operations are tractable , 2005, 20th Annual IEEE Symposium on Logic in Computer Science (LICS' 05).

[2]  Martin C. Cooper,et al.  Constraints, Consistency and Closure , 1998, Artif. Intell..

[3]  Moshe Y. Vardi,et al.  Fixed-Parameter Hierarchies inside PSPACE , 2006, 21st Annual IEEE Symposium on Logic in Computer Science (LICS'06).

[4]  Manuel Bodirsky,et al.  Quantified Equality Constraints , 2007, 22nd Annual IEEE Symposium on Logic in Computer Science (LICS 2007).

[5]  Alex K. Simpson,et al.  Computational Adequacy in an Elementary Topos , 1998, CSL.

[6]  Hubie Chen.  Quantified Constraint Satisfaction, Maximal Constraint Languages, and Symmetric Polymorphisms , 2005, STACS.

[7]  Hubie Chen.  The Computational Complexity of Quantified Constraint Satisfaction , 2004 .

[8]  Peter Jeavons,et al.  Quantified Constraints: Algorithms and Complexity , 2003, CSL.

[9]  Tomás Feder,et al.  The Computational Structure of Monotone Monadic SNP and Constraint Satisfaction: A Study through Datalog and Group Theory , 1999, SIAM J. Comput..

[10]  Georg Gottlob,et al.  The Complexity of Quantified Constraint Satisfaction Problems under Structural Restrictions , 2005, IJCAI.

[11]  Manuel Bodirsky,et al.  Constraint satisfaction with infinite domains , 2004 .

[12]  Peter Jeavons,et al.  The complexity of maximal constraint languages , 2001, STOC '01.

[13]  Manuel Bodirsky,et al.  The Core of a Countably Categorical Structure , 2005, STACS.

[14]  Hubie Chen.  Collapsibility and Consistency in Quantified Constraint Satisfaction , 2004, AAAI.

[15]  Phokion G. Kolaitis,et al.  Conjunctive-query containment and constraint satisfaction , 1998, PODS.

[16]  Peter Jeavons,et al.  Classifying the Complexity of Constraints Using Finite Algebras , 2005, SIAM J. Comput..

[17]  Manuel Bodirsky,et al.  The Complexity of Equality Constraint Languages , 2006, Theory of Computing Systems.

[18]  Andrei A. Bulatov,et al.  A Simple Algorithm for Mal'tsev Constraints , 2006, SIAM J. Comput..

[19]  Wilfrid Hodges,et al.  A Shorter Model Theory , 1997 .

[20]  Albert R. Meyer,et al.  Word problems requiring exponential time(Preliminary Report) , 1973, STOC.

[21]  Andrei A. Bulatov,et al.  A dichotomy theorem for constraints on a three-element set , 2002, The 43rd Annual IEEE Symposium on Foundations of Computer Science, 2002. Proceedings..

[22]  KozenDexter.  Positive first-order logic is NP-complete , 1981 .