Inherent complexity of recursive queries

We give lower bou.nds on the complexity of evaluating Datalog queries; our results delimit the possibility of optimizing such queries by compile-time techniques. The main technical tool is a new class of linear firstorder formulas, whose quantifier depth (respectively, number of variables) measures the sequential (respectively, parallel) complexity of Datalog programs. We define a combinatorial game, and use it to prove nonexpressibility of certain Datalog queries by linear formulas; we thus obtain lower bounds for sequential and for parallel complexity. We prove tight versions of our results, for queries of restricted form, by exploiting uniformity and invariance properties of Datalog programs.

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