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Two-Dimensional Pattern Matching Against Basic Picture Languages

  • František Mráz
  • Daniel PrůšaEmail author
  • Michael Wehar
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11601)

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.

Keywords

Two-dimensional pattern matching Picture languages Local picture languages Two-dimensional finite-state automata 

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • František Mráz
    • 1
  • Daniel Průša
    • 2
    Email author
  • Michael Wehar
    • 3
  1. 1.Faculty of Mathematics and PhysicsCharles UniversityPragueCzech Republic
  2. 2.Faculty of Electrical EngineeringCzech Technical UniversityPragueCzech Republic
  3. 3.Temple UniversityPhiladelphiaUSA

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