Decidability and undecidability results for boundedness of linear recursive queries

If it is possible to eliminate recursion from a Datalog program <italic>P</italic>, then <italic>P</italic> is said to be <italic>bounded</italic>. It was shown by Gaifman et al that the problem of deciding whether a given Datalog program is bounded is undecidable, even for linear programs that has one <italic>4-ary</italic> intensional predicate. We sharpen that result by showing that the problem of deciding whether a given Datalog program is bounded is undecidable, even for linear programs that has one <italic>binary</italic> intensional predicate. We then consider linear programs with a single recursive rule. We show that if the intensional predicate is binary, then the boundedness problem for such program is decidable, in fact, it is NP-complete.

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