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An Improved Homomorphism Preservation Theorem From Lower Bounds in Circuit Complexity
[article]
2016
arXiv
pre-print
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 Φ of quantifier-rank k is preserved under homomorphisms on finite
arXiv:1612.08192v1
fatcat:y23tkqrz6bhwxmslgtmswmew2a