Bounds on the propagation of selection into logic programs

We consider the problem of propagating selections (i.e., bindings of variables) into logic programs. In particular, we study the class of binary chain programs and define selection propagation as the task of finding an equivalent program containing only unary derived predicates. We associate a context free grammar L(H) with every binary chain program H. We show that, given H propagating a selection involving some constant is possible iff L(H) is regular, and therefore undecidable. We also show that propagating a selection of the form p(X,X) is possible iff L(H) is finite, and therefore decidable. We demonstrate the connection of these two cases, respectively, with the weak monadic second order theory of one successor and with monadic generalized spectra. We further clarify the analogy between chain programs and languages from the point of view of program equivalence and selection propagation heuristics.