Homomorphism Problems for First-Order Definable Structures

Authors Bartek Klin, Slawomir Lasota, Joanna Ochremiak, Szymon Torunczyk

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Bartek Klin
Slawomir Lasota
Joanna Ochremiak
Szymon Torunczyk

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Bartek Klin, Slawomir Lasota, Joanna Ochremiak, and Szymon Torunczyk. Homomorphism Problems for First-Order Definable Structures. In 36th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 65, pp. 14:1-14:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)


We investigate several variants of the homomorphism problem: given two relational structures, is there a homomorphism from one to the other? The input structures are possibly infinite, but definable by first-order interpretations in a fixed structure. Their signatures can be either finite or infinite but definable. The homomorphisms can be either arbitrary, or definable with parameters, or definable without parameters. For each of these variants, we determine its decidability status.
  • Sets with atoms
  • first-order interpretations
  • homomorphism problem


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