Decidability and undecidability of equivalence for linear Datalog, with applications to normal-form optimizations

Abstract

A variety of optimizations in logic databases [20] involve the transformation of safe, function-free (Datalog) logic programs to simpler, more efficiently évaluable programs. The essence of these transformations is the detection of program equivalence. Equivalence has been shown to be undecidable in [1, 17, 18, 19], but those results are unsatisfactory in that they involve highly nonlinear rules, or an unbounded number of linear recursive rules, and hence yield no insight into the behaviour of small, linear recursive programs. In this paper, we consider programs that consist of one nonrecursive linear rule, one linear recursive rule and one initialization rule. We provide a tight characterization of the decidability of program equivalence, proving it undecidable for such programs, and proving it decidable for a subclass that includes binary chain programs and programs with no repeated predicates in the rule body. We then apply these results to various normal-form optimizations [12, 18], including the detection of serializability, cornmutativity, basis-linearizability and rule redundancy.