Some results on the complexity of SLD-derivations
In this paper we consider a few simple classes of definite programs and goals and study the problem of deciding whether a given goal has a successful SLD-derivation (the SUCCESS problem). Although the problem is always decidable for the classes studied, it turns out to be NP-complete even for some very simple classes.
The transition between two specific classes of pairs of logic programs and goals (classes C2 and C3) is studied in detail by considering a number of intermediate classes. Some of these belong to the complexity class P while others are NP-Complete. This transition seems to be quite “erratic” in the sense that there is apparently no simple property of the class in consideration that corresponds to NP-hardness.
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