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Preservation Theorems on Sparse Classes Revisited

Authors Anuj Dawar , Ioannis Eleftheriadis

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Author Details

Anuj Dawar
  • Department of Computer Science and Technology, University of Cambridge, UK
Ioannis Eleftheriadis
  • Department of Computer Science and Technology, University of Cambridge, UK

Funding

  • Dawar, Anuj: Funded by UK Research and Innovation (UKRI) under the UK government’s Horizon Europe funding guarantee: grant number EP/X028259/1.
  • Eleftheriadis, Ioannis: Funded by a George and Marie Vergottis Scholarship awarded by Cambridge Trust, an Onassis Foundation Scholarship, and a Robert Sansom Studentship.

Cite AsGet BibTex

Anuj Dawar and Ioannis Eleftheriadis. Preservation Theorems on Sparse Classes Revisited. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 47:1-47:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.MFCS.2024.47

Abstract

We revisit the work studying homomorphism preservation for first-order logic in sparse classes of structures initiated in [Atserias et al., JACM 2006] and [Dawar, JCSS 2010]. These established that first-order logic has the homomorphism preservation property in any sparse class that is monotone and addable. It turns out that the assumption of addability is not strong enough for the proofs given. We demonstrate this by constructing classes of graphs of bounded treewidth which are monotone and addable but fail to have homomorphism preservation. We also show that homomorphism preservation fails on the class of planar graphs. On the other hand, the proofs of homomorphism preservation can be recovered by replacing addability by a stronger condition of amalgamation over bottlenecks. This is analogous to a similar condition formulated for extension preservation in [Atserias et al., SiCOMP 2008].

Subject Classification

ACM Subject Classification
  • Theory of computation → Finite Model Theory
Keywords
  • Homomorphism preservation
  • sparsity
  • finite model theory
  • planar graphs

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References

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