2 Search Results for "Ham, Lucy"

Document
DOI: 10.4230/LIPIcs.CSL.2025.6
Equi-Rank Homomorphism Preservation Theorem on Finite Structures

Authors: Benjamin Rossman

Published in: LIPIcs, Volume 326, 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)

Abstract
The Homomorphism Preservation Theorem (HPT) of classical model theory states that a first-order sentence is preserved under homomorphisms if, and only if, it is equivalent to an existential-positive sentence. This theorem remains valid when restricted to finite structures, as demonstrated by the author in [Rossman, 2008; Rossman, 2017] via distinct model-theoretic and circuit-complexity based proofs. In this paper, we present a third (and significantly simpler) proof of the finitary HPT based on a generalized Cai-Fürer-Immerman construction. This method establishes a tight correspondence between syntactic parameters of a homomorphism-preserved sentence (quantifier rank, variable width, alternation height) and structural parameters of its minimal models (tree-width, tree-depth, decomposition height). Consequently, we prove a conjectured "equi-rank" version of the finitary HPT. In contrast, previous versions of the finitary HPT possess additional properties, but incur blow-ups in the quantifier rank of the equivalent existential-positive sentence.
Cite as

Benjamin Rossman. Equi-Rank Homomorphism Preservation Theorem on Finite Structures. In 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 326, pp. 6:1-6:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{rossman:LIPIcs.CSL.2025.6,
  author =	{Rossman, Benjamin},
  title =	{{Equi-Rank Homomorphism Preservation Theorem on Finite Structures}},
  booktitle =	{33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)},
  pages =	{6:1--6:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-362-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{326},
  editor =	{Endrullis, J\"{o}rg and Schmitz, Sylvain},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2025.6},
  URN =		{urn:nbn:de:0030-drops-227634},
  doi =		{10.4230/LIPIcs.CSL.2025.6},
  annote =	{Keywords: finite model theory, preservation theorems, quantifier rank}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2016.36
A Gap Trichotomy for Boolean Constraint Problems: Extending Schaefer's Theorem

Authors: Lucy Ham

Published in: LIPIcs, Volume 64, 27th International Symposium on Algorithms and Computation (ISAAC 2016)

Abstract
In this paper, we investigate "gap problems", which are promise problems where YES instances are flexibly satisfiable in a certain sense, and NO instances are not satisfiable at all. These gap problems generalise a family of constraint-related decision problems, including the constraint satisfaction problem itself, the separation problem (can distinct variables be validly assigned distinct values?) and the 2-robust satisfiability problem (does any assignment on two variables extend to a full satisfying assignment?). We establish a Gap Trichotomy Theorem, which on Boolean domains, completely classifies the complexity of the gap problems considered. As a consequence, we obtain several well-known dichotomy results, as well as dichotomies for the separation problem and the 2-robust satisfiability problem: all are either polynomial-time tractable or NP-complete. Schaefer’s original dichotomy is a notable particular case.
Cite as

Lucy Ham. A Gap Trichotomy for Boolean Constraint Problems: Extending Schaefer's Theorem. In 27th International Symposium on Algorithms and Computation (ISAAC 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 64, pp. 36:1-36:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

Copy BibTex To Clipboard

@InProceedings{ham:LIPIcs.ISAAC.2016.36,
  author =	{Ham, Lucy},
  title =	{{A Gap Trichotomy for Boolean Constraint Problems: Extending Schaefer's Theorem}},
  booktitle =	{27th International Symposium on Algorithms and Computation (ISAAC 2016)},
  pages =	{36:1--36:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-026-2},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{64},
  editor =	{Hong, Seok-Hee},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2016.36},
  URN =		{urn:nbn:de:0030-drops-68060},
  doi =		{10.4230/LIPIcs.ISAAC.2016.36},
  annote =	{Keywords: Constraint Satisfaction Problem, Robust satisfiability, Clone theory, Dichotomy, Trichotomy, Boolean}
}
  • Refine by Type
  • 2 Document/PDF
  • 1 Document/HTML

  • Refine by Publication Year
  • 1 2025
  • 1 2016

  • Refine by Author
  • 1 Ham, Lucy
  • 1 Rossman, Benjamin

  • Refine by Series/Journal
  • 2 LIPIcs

  • Refine by Classification
  • 1 Theory of computation → Finite Model Theory

  • Refine by Keyword
  • 1 Boolean
  • 1 Clone theory
  • 1 Constraint Satisfaction Problem
  • 1 Dichotomy
  • 1 Robust satisfiability
  • Show More...

Any Issues?
X

Feedback on the Current Page

CAPTCHA

Thanks for your feedback!

Feedback submitted to Dagstuhl Publishing

Could not send message

Please try again later or send an E-mail
© 2023-2026 Schloss Dagstuhl – LZI GmbH Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact