Document Open Access Logo

An Improved Homomorphism Preservation Theorem From Lower Bounds in Circuit Complexity

Author Benjamin Rossman

PDF

File

Thumbnail PDF
PDF
LIPIcs.ITCS.2017.27.pdf
  • Filesize: 0.65 MB
  • 17 pages

Document Identifiers

Subject Classification

Keywords
  • circuit complexity
  • finite model theory

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
    0
    Metadata Views

Abstract

Previous work of the author [Rossmann'08] 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 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 poly(k). Quantitatively, this improves the result of [Rossmann'08], where the upper bound on quantifier-rank is a non-elementary function of k.

Cite As Get BibTex

Benjamin Rossman. An Improved Homomorphism Preservation Theorem From Lower Bounds in Circuit Complexity. In 8th Innovations in Theoretical Computer Science Conference (ITCS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 67, pp. 27:1-27:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017) https://doi.org/10.4230/LIPIcs.ITCS.2017.27

Author Details

Benjamin Rossman
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2025 Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact