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Publications [#348672] of Benjamin Rossman

Papers Published

  1. Rossman, B, An improved homomorphism preservation theorem from lower bounds in circuit complexity, Leibniz International Proceedings in Informatics, Lipics, vol. 67 (November, 2017), ISBN 9783959770293 [doi]
    (last updated on 2022/05/21)

    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 AC0 formula size of the colored subgraph isomorphism problem. Formally, we show the following: if a first-order sentence φ of quantifier-rank k is preserved under homomorphisms on finite structures, then it is equivalent on finite structures to an existential-positive sentence of quantifier-rank kO(1). Quantitatively, this improves the result of [39], where the upper bound on the quantifier-rank of is a non-elementary function of k.
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