Deciding boundedness of monadic sirups

Stanislav Kikot; Agi Kurucz; Vladimir Podolskii; Michael Zakharyaschev

doi:10.1145/3452021.3458332

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arXiv · 2108.00433

Deciding boundedness of monadic sirups

Stanislav Kikot·Agi Kurucz·Vladimir Podolskii·Michael Zakharyaschev

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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.

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Stanislav Kikot, Agi Kurucz, Vladimir Podolskii, Michael Zakharyaschev. 2021-08-01. Deciding boundedness of monadic sirups. https://doi.org/10.1145/3452021.3458332

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