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Automatic Equivalence Structures of Polynomial Growth

Authors Moses Ganardi, Bakhadyr Khoussainov

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Author Details

Moses Ganardi
  • University of Siegen, Siegen, Germany
Bakhadyr Khoussainov
  • University of Auckland, Auckland, New Zealand

Funding

  • Ganardi, Moses: This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 731143.

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Moses Ganardi and Bakhadyr Khoussainov. Automatic Equivalence Structures of Polynomial Growth. In 28th EACSL Annual Conference on Computer Science Logic (CSL 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 152, pp. 21:1-21:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020) https://doi.org/10.4230/LIPIcs.CSL.2020.21

Abstract

In this paper we study the class EqP of automatic equivalence structures of the form ?=(D, E) where the domain D is a regular language of polynomial growth and E is an equivalence relation on D. Our goal is to investigate the following two foundational problems (in the theory of automatic structures) aimed for the class EqP. The first is to find algebraic characterizations of structures from EqP, and the second is to investigate the isomorphism problem for the class EqP. We provide full solutions to these two problems. First, we produce a characterization of structures from EqP through multivariate polynomials. Second, we present two contrasting results. On the one hand, we prove that the isomorphism problem for structures from the class EqP is undecidable. On the other hand, we prove that the isomorphism problem is decidable for structures from EqP with domains of quadratic growth.

Subject Classification

ACM Subject Classification
  • Theory of computation → Formal languages and automata theory
Keywords
  • automatic structures
  • polynomial growth
  • isomorphism problem

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