Logic in Computer Science, Symposium on (2007)

Wroclaw, Poland

July 10, 2007 to July 14, 2007

ISSN: 1043-6871

ISBN: 0-7695-2908-9

pp: 193-202

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/LICS.2007.47

L?szl? Egri , McGill University, Canada

Pascal Tesson , Laval University, Canada

Benoit Larose , Concordia University, Canada

ABSTRACT

We introduce symmetric Datalog, a syntactic restriction of linear Datalog and show that its expressive power is exactly that of restricted symmetric Krom monotone SNP. The deep result of Reingold [17] on the complexity of undirected connectivity suffices to show that symmetric Datalog queries can be evaluated in logarithmic space. We show that for a number of constraint languages \Gamma, the complement of the constraint satisfaction problem CSP(\Gamma) can be expressed in symmetric Datalog. In particular, we show that if CSP(\Gamma) is first-order definable and \Lambda is a finite subset of the relational clone generated by \Gamma then ?CSP(\Lambda) is definable in symmetric Datalog. Over the two-element domain and under standard complexity-theoretic assumptions, expressibility of ?CSP(\Gamma) in symmetric Datalog corresponds exactly to the class of CSPs computable in logarithmic space. Finally, we describe a fairly general subclass of implicational (or 0/1/all) constraints for which the complement of the corresponding CSP is also definable in symmetric Datalog. Our results provide preliminary evidence that symmetric Datalog may be a unifying explanation for families of CSPs lying in L.

INDEX TERMS

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CITATION

L?szl? Egri,
Pascal Tesson,
Benoit Larose,
"Symmetric Datalog and Constraint Satisfaction Problems in Logspace",

*Logic in Computer Science, Symposium on*, vol. 00, no. , pp. 193-202, 2007, doi:10.1109/LICS.2007.47