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Two-Dimensional Pattern Matching Against Basic Picture Languages

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Implementation and Application of Automata (CIAA 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11601))

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Abstract

Given a two-dimensional array of symbols and a picture language over a finite alphabet, we study the problem of finding rectangular subarrays of the array that belong to the picture language. We formulate four particular problems – finding maximum, minimum, any or all match(es) – and describe algorithms solving them for basic classes of picture languages, including local picture languages and picture languages accepted by deterministic on-line tessellation automata or deterministic four-way finite automata. We also prove that the matching problems cannot be solved for the class of local picture languages in linear time unless the problem of triangle finding is solvable in quadratic time. This shows there is a fundamental difference in the pattern matching complexity regarding the one-dimensional and two-dimensional setting.

D. Průša—Supported by the Czech Science Foundation grant 19-09967S.

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Notes

  1. 1.

    E.g. the local picture languages \(L_\mathrm{corn}\) and \(L_\mathrm{corn2}\) are not in \(\mathsf{bu\text {-}LOC} \).

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Authors and Affiliations

  1. Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic

    František Mráz

  2. Faculty of Electrical Engineering, Czech Technical University, Prague, Czech Republic

    Daniel Průša

  3. Temple University, Philadelphia, PA, USA

    Michael Wehar

Authors
  1. František Mráz
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  2. Daniel Průša
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  3. Michael Wehar
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Correspondence to Daniel Průša .

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Editors and Affiliations

  1. Slovak Academy of Sciences, Košice, Slovakia

    Michal Hospodár

  2. Slovak Academy of Sciences, Košice, Slovakia

    Galina Jirásková

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Mráz, F., Průša, D., Wehar, M. (2019). Two-Dimensional Pattern Matching Against Basic Picture Languages. In: Hospodár, M., Jirásková, G. (eds) Implementation and Application of Automata. CIAA 2019. Lecture Notes in Computer Science(), vol 11601. Springer, Cham. https://doi.org/10.1007/978-3-030-23679-3_17

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  • DOI: https://doi.org/10.1007/978-3-030-23679-3_17

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