Deciding boundedness of monadic sirups

TL;DR

This paper proves that determining boundedness (FO-rewritability) of monadic sirups is 2Exp-hard, resolving a long-standing open problem and advancing the classification of disjunctive sirups based on data complexity.

Contribution

It establishes the 2Exp-hardness of FO-rewritability for monadic sirups and advances the classification of disjunctive sirups' evaluation complexity.

Findings

Deciding boundedness of monadic sirups is 2Exp-hard.

Deciding FO-rewritability of disjunctive sirups with dag-shaped queries is 2Exp-hard.

Progress towards FO/L-hardness dichotomy for disjunctive sirups with ditree-shaped queries.

Abstract

We show that deciding boundedness (aka FO-rewritability) of monadic single rule datalog programs (sirups) is 2Exp-hard, which matches the upper bound known since 1988 and finally settles a long-standing open problem. We obtain this result as a byproduct of an attempt to classify monadic `disjunctive sirups' -- Boolean conjunctive queries q with unary and binary predicates mediated by a disjunctive rule T(x)vF(x) <- A(x) -- according to the data complexity of their evaluation. Apart from establishing that deciding FO-rewritability of disjunctive sirups with a dag-shaped q is also 2Exp-hard, we make substantial progress towards obtaining a complete FO/L-hardness dichotomy of disjunctive sirups with ditree-shaped q.