Abstract
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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Matz, O. (1998). On piecewise testable, starfree, and recognizable picture languages. In: Nivat, M. (eds) Foundations of Software Science and Computation Structures. FoSSaCS 1998. Lecture Notes in Computer Science, vol 1378. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0053551
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DOI: https://doi.org/10.1007/BFb0053551
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