Abstract
We show that the language of pictures over {a, b}, where all occurring b's are connected is recognizable, which solves an open problem in [Mat98]. We generalize the used construction to show that monocausal deterministically recognizable picture languages are recognizable, which is surprisingly nontrivial. Furthermore we show that the language of pictures over {a, b}, where the number of a's is equal to the number of b's is nonuniformly recognizable.
This research has been supported by the DFG Project La 618/3-1 KOMET.
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References
E. Allender and K. Reinhardt. Isolation matching and counting. to appear in Proc. of 13th Computational Complexity, 1998.
Ronald Fagin, Larry J. Stockmeyer, and Moshe Y. Vardi. On monadic NP vs. monadic co-NP. Information and Computation, 120(1):78–92, July 1995.
Martin Fürer. The tight deterministic time hierarchy. In Proceedings of the Fourteenth Annual ACM Symposium on Theory of Computing, pages 8–16, San Francisco, California, 5–7 May 1982.
D. Giammarresi and A. Restivo. Two-dimensional languages. In G. Rozenberg and A. Salomaa, editors, Handbook of Formal Language Theory, volume III. Springer-Verlag, New York, 1996.
Dora Giammarresi, Antonio Restivo, Sebastian Seibert, and Wolfgang Thomas. Monadic second-order logic over pictures and recognizability by tiling systems. In P. Enjalbert, E.W. Mayr, and K.W. Wagner, editors, Proceedings of the 11th Annual Symposium on Theoretical Aspects of Computer Science, STACS 94 (Caen, France, February 1994), LNCS 775, pages 365–375, Berlin-Heidelberg-New York-LondonParis-Tokyo-Hong Kong-Barcelona-Budapest, 1994. Springer-Verlag.
K. Inoue and A. Nakamura. Some properties of two-dimensional on-line tessellation acceptors. Information Sciences, 13:95–121, 1977.
Oliver Matz. Regular expressions and context-free grammars for picture languages. In 14th Annual Symposium on Theoretical Aspects of Computer Science, volume 1200 of lncs, pages 283–294, Lübeck, Germany, 27 February–March 1 1997. Springer.
Oliver Matz. On piecewise testable, starfree, and recognizable picture languages. In Maurice Nivat, editor, Foundations of Software Science and Computation Structures, volume 1378 of Lecture Notes in Computer Science, pages 203–210. Springer, 1998.
K. Reinhardt and E. Allender. Making nondeterminism unambiguous. In 38 th IEEE Symposium on Foundations of Computer Science (FOCS), pages 244–253, 1997.
Thomas Wilke. Star-free picture expressions are strictly weaker than firstorder logic. In Pierpaolo Degano, Roberto Gorrieri, and Alberto Marchetti-Spaccamela, editors, Automata, Languages and Programming, volume 1256 of Lect. Notes Comput. Sci., pages 347–357, Bologna, Italy, 1997. Springer.
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Reinhardt, K. (1998). On some recognizable picture-languages. In: Brim, L., Gruska, J., Zlatuška, J. (eds) Mathematical Foundations of Computer Science 1998. MFCS 1998. Lecture Notes in Computer Science, vol 1450. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0055827
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DOI: https://doi.org/10.1007/BFb0055827
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