On piecewise testable, starfree, and recognizable picture languages

  • Oliver Matz
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1378)


We isolate a technique for showing that a picture language (i.e. a“two-dimensional language/rd) is not recognizable. Then we prove the non-recognizability of a picture language that is both starfree (i.e., definable by means of union, concatenation, and complement) and piecewise testable (i.e., definable by means of allowed subpictures), solving an open question in [GR96].

We also define local, locally testable, and locally threshold testable picture languages and summarize known inclusion results for these classes. The classes of piecewise testable, locally testable, and locally threshold testable picture languages can, as in the word case, be characterized by certain (fragments of) first-order logics.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Oliver Matz
    • 1
  1. 1.Institut für Informatik und Praktische MathematikChristian-Albrechts-Universität KielKielGermany

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