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State Complexity of Union and Intersection on Graph-Walking Automata

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Descriptional Complexity of Formal Systems (DCFS 2021)

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Abstract

Finite automata traversing graphs by moving along their edges are known as graph-walking automata (GWA). This paper investigates the state complexity of union and intersection for this model. It is proved that the union of GWA with m and n states, with \(m \leqslant n\), operating on graphs with k labels of edge end-points, is representable by a GWA with \(2km+n+1\) states, and at least \(2(k-3)(m-1)+n-1\) states are necessary in the worst case. For the intersection, the upper bound is \((2k+1)m+n\) and the lower bound is \(2(k-3)(m-1)+n-1\).

This work was supported by the Russian Science Foundation, project 18-11-00100.

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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

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  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. Yonsei University, Seoul, Korea (Republic of)

    Yo-Sub Han

  2. Kangwon National University, Chuncheon, Korea (Republic of)

    Sang-Ki Ko

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Martynova, O., Okhotin, A. (2021). State Complexity of Union and Intersection on Graph-Walking Automata. In: Han, YS., Ko, SK. (eds) Descriptional Complexity of Formal Systems. DCFS 2021. Lecture Notes in Computer Science(), vol 13037. Springer, Cham. https://doi.org/10.1007/978-3-030-93489-7_11

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  • DOI: https://doi.org/10.1007/978-3-030-93489-7_11

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  • Online ISBN: 978-3-030-93489-7

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