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Monadic second-order logic over pictures and recognizability by tiling systems

  • Dora Giammarresi
  • Sebastian Seibert
  • Antonio Restivo
  • Wolfgang Thomas
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 775)

Abstract

We show that a set of pictures (rectangular arrays of symbols) is recognized by a finite tiling system if and only if it is definable in existential monadic second-order logic. As a consequence, finite tiling systems constitute a notion of recognizability over two-dimensional inputs which at the same time generalizes finite-state recognizability over strings and matches a natural logic. The proof is based on the Ehrenfeucht-FraÏssé technique for first-order logic and an implementation of “threshold counting” within tiling systems.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Dora Giammarresi
    • 1
  • Sebastian Seibert
    • 2
  • Antonio Restivo
    • 1
  • Wolfgang Thomas
    • 2
  1. 1.Dipartimento di Matematica ed ApplicazioniUniversità di PalermoPalermoItaly
  2. 2.Institut für Informatik und Praktische MathematikChristian-Albrechts-UniversitätKiel

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