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Designing Dependencies


Given a binary recursively enumerable relation R, one or more logic programs over a language L can be constructed and interconnected to produce a dependency relation D on selected predicates within the Herbrand base BL of L isomorphic to R. D can be, optionally, a positive, negative or mixed dependency relation. The construction is applied to representing any effective game of the type introduced by Gurevich and Harrington, which they used to prove Rabin's decision method for S2S, as the dependency relation of a logic program. We allow games over an infinite alphabet of possible moves. We use this representation to reveal a common underlying reason, having to do with the shape of a program's dependency relation, for the complexity of several logic program properties.