The Logic of Counting Query Answers: A Study via Existential Positive Queries

We consider the computational complexity of counting the number of answers to a logical formula on a finite structure. In the setting of parameterized complexity, we present a trichotomy theorem on classes of existential positive queries. We then proceed to study an extension of first-order logic in which algorithms for the counting problem at hand can be naturally and conveniently expressed.

[1]  Hubie Chen,et al.  The Tractability Frontier of Graph-Like First-Order Query Sets , 2014, J. ACM.

[2]  Ashok K. Chandra,et al.  Optimal implementation of conjunctive queries in relational data bases , 1977, STOC '77.

[3]  Phokion G. Kolaitis,et al.  Constraint Satisfaction, Bounded Treewidth, and Finite-Variable Logics , 2002, CP.

[4]  Jörg Flum,et al.  Parameterized Complexity Theory , 2006, Texts in Theoretical Computer Science. An EATCS Series.

[5]  Peter Jonsson,et al.  The complexity of counting homomorphisms seen from the other side , 2004, Theor. Comput. Sci..

[6]  Serge Abiteboul,et al.  Foundations of Databases , 1994 .

[7]  Hubie Chen,et al.  A Trichotomy in the Complexity of Counting Answers to Conjunctive Queries , 2014, ICDT.

[8]  Francesco Scarcello,et al.  Counting solutions to conjunctive queries: structural and hybrid tractability , 2014, SEBD.

[9]  Hubie Chen,et al.  On the complexity of existential positive queries , 2012, ACM Trans. Comput. Log..

[10]  Mihalis Yannakakis,et al.  On the Complexity of Database Queries , 1999, J. Comput. Syst. Sci..

[11]  Hans L. Bodlaender.  A linear time algorithm for finding tree-decompositions of small treewidth , 1993, STOC '93.

[12]  Fedor V. Fomin,et al.  Exact exponential algorithms , 2013, CACM.

[13]  Martin Grohe,et al.  The complexity of homomorphism and constraint satisfaction problems seen from the other side , 2003, 44th Annual IEEE Symposium on Foundations of Computer Science, 2003. Proceedings..

[14]  Reinhard Pichler,et al.  Tractable Counting of the Answers to Conjunctive Queries , 2013, AMW.

[15]  Moshe Y. Vardi.  On the Complexity of Bounded-Variable Queries. , 1995, PODS 1995.

[16]  Arnaud Durand,et al.  Structural Tractability of Counting of Solutions to Conjunctive Queries , 2013, ICDT '13.