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Recognition and Complexity Results for Projection Languages of Two-Dimensional Automata

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Descriptional Complexity of Formal Systems (DCFS 2020)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12442))

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Abstract

The row projection (resp., column projection) of a given two-dimensional language L is the one-dimensional language consisting of first rows (resp., first columns) of all two-dimensional words in L. The operation of row projection has previously been studied under the name “frontier language”, and previous work in this area has focused primarily on one- and two-dimensional language classes.

In this paper, we study projections of languages recognized by various two-dimensional automaton classes. We show that both the row and column projections of languages recognized by (four-way) two-dimensional automata are exactly context-sensitive. We also show that the column projections of languages recognized by unary three-way two-dimensional automata can be recognized using nondeterministic logspace. Finally, we study the state complexity of projection languages for two-way two-dimensional automata, focusing on the language operations of union and diagonal concatenation.

Smith and Salomaa were supported by Natural Sciences and Engineering Research Council of Canada Grant OGP0147224.

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Authors and Affiliations

  1. School of Computing, Queen’s University, Kingston, ON, K7L 2N8, Canada

    Taylor J. Smith & Kai Salomaa

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  1. Taylor J. Smith
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  2. Kai Salomaa
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Correspondence to Taylor J. Smith or Kai Salomaa .

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Editors and Affiliations

  1. Slovak Academy of Sciences, Košice, Slovakia

    Galina Jirásková

  2. University of Milan, Milan, Italy

    Giovanni Pighizzini

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Smith, T.J., Salomaa, K. (2020). Recognition and Complexity Results for Projection Languages of Two-Dimensional Automata. In: Jirásková, G., Pighizzini, G. (eds) Descriptional Complexity of Formal Systems. DCFS 2020. Lecture Notes in Computer Science(), vol 12442. Springer, Cham. https://doi.org/10.1007/978-3-030-62536-8_17

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  • DOI: https://doi.org/10.1007/978-3-030-62536-8_17

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  • Print ISBN: 978-3-030-62535-1

  • Online ISBN: 978-3-030-62536-8

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