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Homomorphisms on Graph-Walking Automata

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Implementation and Application of Automata (CIAA 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13266))

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Abstract

Graph-walking automata (GWA) analyze an input graph by moving between its nodes, following the edges. This paper investigates the effect of node-replacement graph homomorphisms on recognizability by these automata. The family of graph languages recognized by GWA is closed under inverse homomorphisms. The main result of this paper is that, for n-state automata operating on graphs with k labels of edge end-points, the inverse homomorphic images require GWA with \(kn+O(1)\) states in the worst case. The second result is that already for tree-walking automata, the family they recognize is not closed under injective homomorphisms; here the proof is based on a homomorphic characterization of regular tree languages.

This work was supported by the Ministry of Science and Higher Education of the Russian Federation, agreement 075-15-2019-1619.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, St. Petersburg State University, 14th Line V.O., 29, Saint Petersburg, 199178, Russia

    Olga Martynova & Alexander Okhotin

  2. Leonhard Euler International Mathematical Institute at St. Petersburg State University, Saint Petersburg, Russia

    Olga Martynova

Authors
  1. Olga Martynova
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  2. Alexander Okhotin
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Correspondence to Alexander Okhotin .

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Editors and Affiliations

  1. UFR. des Sciences et Techniques, University of Rouen, Saint-Étienne du Rouvray Cedex, France

    Pascal Caron

  2. UFR. des Sciences et Techniques, University of Rouen, Saint-Étienne du Rouvray Cedex, France

    Ludovic Mignot

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Martynova, O., Okhotin, A. (2022). Homomorphisms on Graph-Walking Automata. In: Caron, P., Mignot, L. (eds) Implementation and Application of Automata. CIAA 2022. Lecture Notes in Computer Science, vol 13266. Springer, Cham. https://doi.org/10.1007/978-3-031-07469-1_14

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  • DOI: https://doi.org/10.1007/978-3-031-07469-1_14

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-07468-4

  • Online ISBN: 978-3-031-07469-1

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