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- W4300030863 abstract "Previous work of the author [39] showed that the Homomorphism Preservation Theorem of classical model theory remains valid when its statement is restricted to finite structures. In this paper, we give a new proof of this result via a reduction to lower bounds in circuit complexity, specifically on the AC$^0$ formula size of the colored subgraph isomorphism problem. Formally, we show the following: if a first-order sentence $Phi$ of quantifier-rank $k$ is preserved under homomorphisms on finite structures, then it is equivalent on finite structures to an existential-positive sentence $Psi$ of quantifier-rank $k^{O(1)}$. Quantitatively, this improves the result of [39], where the upper bound on the quantifier-rank of $Psi$ is a non-elementary function of $k$." @default.
- W4300030863 created "2022-10-03" @default.
- W4300030863 creator A5007686466 @default.
- W4300030863 date "2016-12-24" @default.
- W4300030863 modified "2023-09-26" @default.
- W4300030863 title "An Improved Homomorphism Preservation Theorem From Lower Bounds in Circuit Complexity" @default.
- W4300030863 doi "https://doi.org/10.48550/arxiv.1612.08192" @default.
- W4300030863 hasPublicationYear "2016" @default.
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