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arXiv · 2504.08914

Circuits and Formulas for Datalog over Semirings

Austen Z. Fan·Paraschos Koutris·Sudeepa Roy
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Abstract

In this paper, we study circuits and formulas for provenance polynomials of Datalog programs. We ask the following question: given an absorptive semiring and a fact of a Datalog program, what is the optimal depth and size of a circuit/formula that computes its provenance polynomial? We focus on absorptive semirings as these guarantee the existence of a polynomial-size circuit. Our main result is a dichotomy for several classes of Datalog programs on whether they admit a formula of polynomial size or not. We achieve this result by showing that for these Datalog programs the optimal circuit depth is either $\Theta(\log m)$ or $\Theta(\log^2 m)$, where $m$ is the input size. We also show that for Datalog programs with the polynomial fringe property, we can always construct low-depth circuits of size $O(\log^2 m)$. Finally, we give characterizations of when Datalog programs are bounded over more general semirings.

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Austen Z. Fan, Paraschos Koutris, Sudeepa Roy. 2025-04-11. Circuits and Formulas for Datalog over Semirings. https://arxiv.org/abs/2504.08914

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