We consider the problem of propagating selections into logic programs (i.e., recursive Horn clause programs). In particular, we study the class of chain programs and formalize selection propagation on such a logic program as: the task of finding an equivalent program containing only monadic derived predicates. Selection propagation is always possible for database programs (i.e., tirst-order formula programs) and is often a desirable optimization. We show that the situation is qualitatively

more »

... qualitatively different for logic programs. We associate a context free language L(H) with every 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 context-free languages from the point of view of program equivalence, first-order expressibility over finite structures, and selection propagation heuristics.