Constraint satisfaction problems in non-deterministic logarithmic space

Abstract

We study which constraint satisfaction problems (CSPs) are solvable in NL. In particular, we identify a general condition called bounded path duality, that explains all the families of CSPs previously known to be in NL. Bounded path duality captures the class of constraint satisfaction problems that can be solved by linear Datalog programs, i.e., Datalog programs with at most one IDBin the body of each rule. We obtain several alternative characterizations of bounded path duality. We also address the problem of deciding which constraint satisfaction problems have bounded path duality. In this direction we identify a subclass of bounded path duality problems, called (1,k)-path duality problems for which membership is decidable. Finally, we study which closure operations guarantee bounded path duality. We show that closure under any operation in the pseudovariety generated by the class of dual discriminator operations is a sufficient condition for bounded path duality. © 2002 Springer-Verlag Berlin Heidelberg.