Superfiniteness of Query Answers in Deductive Databases: An Automata-Theoretic Approach

Deciding finiteness of query answers is a problem of fundamental importance to query systems supporting declarative logic based languages with function symbols. Unfortunately, this problem is undecidable in general. One of the recently proposed techniques for coping with this situation consists in (i) approximating the original program with function symbols by a datalog program with infinite base relations, together with finiteness constraints (fcs) acting on them (fcs say that if certain columns of a relation are finite, so are other columns), and (ii) using an approximation for finiteness, called superfiniteness. A query is finite if it has finite answers in the least fixpoint model of the program, whereas it is superfinite if it has a finite answer in every fixpoint model of the program. While superfiniteness is decidable, the only known procedure for it takes time exponential in the size of the program and associated constraints. The main contribution of this paper is the development of automata-theoretic techniques for superfiniteness analysis and polynomial time decision procedures for certain classes of linear programs in the presence of unary fcs.

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