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In the present article logic programs (both with and without negation) that do not use functional symbols are studied. Three algorithmic problems for functional symbol-free programs are investigated: the existence of a solvable interpreter, the problem of Δ-equivalence and the problem of logical equivalence. The first two problems are known to be decidable for functional symbol-free definite programs. We show that the third one is also decidable for such programs. In contrast, all three problems are shown to be undedicable for functional symbol-free general programs.