Symmetric Datalog and Constraint Satisfaction Problems in Logspace

We introduce symmetric Datalog, a syntactic restriction of linear Datalog and show that its expressive power is exactly that of restricted symmetric monotone Krom 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 Γ, the complement of the constraint satisfaction problem CSP(Γ) can be expressed in symmetric Datalog. In particular, we show that if CSP(Γ) is first-order definable and Λ is a finite subset of the relational clone generated by Γ then ¬CSP(Λ) is definable in symmetric Datalog. Over the two-element domain and under a standard complexity-theoretic assumption, expressibility of ¬CSP(Γ) in symmetric Datalog corresponds exactly to the class of CSPs solvable in logarithmic space. Finally, we describe a fairly general subclass of implicational (or 0/1/all) constraints for which the complement of the co...

• Type: Conference
• Year: 2007
• Where: LICS
• Authors: László Egri, Benoit Larose, Pascal Tesson
• Keywords: Computer Science, LICS 2007, Symmetric Datalog, Symmetric Datalog Corresponds, Symmetric Datalog Queries