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Weighted Picture Automata and Weighted Logics

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STACS 2006 (STACS 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3884))

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Abstract

The theory of two-dimensional languages, generalizing formal string languages, was motivated by problems arising from image processing and models of parallel computing. Weighted automata and series over pictures map pictures to some semiring and provide an extension to a quantitative setting. We establish a notion of a weighted MSO logics over pictures. The semantics of a weighted formula will be a picture series. We introduce weighted 2-dimensional online tessellation automata (W2OTA) extending the common automata-theoretic model for picture languages. We prove that the class of picture series defined by sentences of the weighted logics coincides with the family of picture series that are computable by W2OTA. Moreover, behaviours of W2OTA coincide precisely with the recognizable picture series characterized in [18].

Supported by the GK 446/3 of the German Research Foundation.

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References

  1. Berstel, J., Reutenauer, C.: Rational Series and Their Languages. EATCS Monographs on Theoretical Computer Science, vol. 12. Springer, Heidelberg (1984)

    MATH  Google Scholar 

  2. Blum, M., Hewitt, C.: Automata on a 2-dimensional tape. In: IEEE Symposium on Switching and Automata Theory, pp. 155–160 (1967)

    Google Scholar 

  3. Bozapalidis, S., Grammatikopoulou, A.: Recognizable picture series. In: special volume on Weighted Automata, presented at WATA 2004, Dresden. Journal of Automata, Languages and Combinatorics (in print, 2005)

    Google Scholar 

  4. Droste, M., Gastin, P.: Weighted automata and weighted logics. In: Caires, L., Italiano, G.F., Monteiro, L., Palamidessi, C., Yung, M. (eds.) ICALP 2005. LNCS, vol. 3580, pp. 513–525. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  5. Droste, M., Vogler, H.: Weighted tree automata and weighted logics (submitted, 2005)

    Google Scholar 

  6. Dubois, D., Hüllermeier, E., Prade, H.: A systematic approach to the assessment of fuzzy association rules. Technical report, Philipps-Universität Marburg (2004)

    Google Scholar 

  7. Eilenberg, S.: Automata, Languages, and Machines, vol. A. Academic Press, New (1974)

    MATH  Google Scholar 

  8. Fu, K.S.: Syntactic Methods in Pattern Recognition. Academic Press, New York (1974)

    MATH  Google Scholar 

  9. Giammarresi, D., Restivo, A.: Recognizable picture languages. International Journal Pattern Recognition and Artificial Intelligence 6(2-3), 31–46 (1992); Issue on Parallel Image Processing. Nivat, M., Saoudi, A., Wangs, P.S.P. (eds.)

    MATH  Google Scholar 

  10. Giammarresi, D., Restivo, A.: Two-dimensional finite state recognizability. Fundam. Inform. 25(3), 399–422 (1996)

    MathSciNet  MATH  Google Scholar 

  11. Giammarresi, D., Restivo, A.: Two-dimensional languages. In: Rozenberg, G., Salomaa, A. (eds.) Handbook of Formal Languages. Beyond Words, vol. 3, pp. 215–267. Springer, Berlin (1997)

    Chapter  Google Scholar 

  12. Giammarresi, D., Restivo, A., Seibert, S., Thomas, W.: Monadic second-order logic over rectangular pictures and recognizability by tiling systems. Information and Computation 125, 32–45 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  13. Inoue, K., Nakamura, A.: Some properties of two-dimensional on-line tessellation acceptors. Information Sciences 13, 95–121 (1977)

    Article  MathSciNet  MATH  Google Scholar 

  14. Kuich, W., Salomaa, A.: Semirings, Automata, Languages. EATCS Monographs in Theoretical Computer Science, vol. 6. Springer, Berlin (1986)

    Book  MATH  Google Scholar 

  15. Latteux, M., Simplot, D.: Recognizable picture languages and domino tiling. Theoretical Computer Science 178, 275–283 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  16. Matz, O.: On piecewise testable, starfree, and recognizable picture languages. In: Nivat, M. (ed.) ETAPS 1998 and FOSSACS 1998. LNCS, vol. 1378, pp. 203–210. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  17. Mäurer, I.: Characterizations of weighted picture series (in preparation, 2005)

    Google Scholar 

  18. Mäurer, I.: Recognizable and rational picture series. In: Conference on Algebraic Informatics, pp. 141–155. Aristotle University of Thessaloniki Press (2005)

    Google Scholar 

  19. Minski, M., Papert, S.: Perceptron. M.I.T. Press, Cambridge (1969)

    Google Scholar 

  20. Salomaa, A., Soittola, M.: Automata-Theoretic Aspects of Formal Power Series. Texts and Monographs on Computer Science. Springer, Heidelberg (1978)

    Book  MATH  Google Scholar 

  21. Thomas, W.: On logics, tilings, and automata. In: Leach Albert, J., Monien, B., Rodríguez-Artalejo, M. (eds.) ICALP 1991. LNCS, vol. 510, pp. 441–453. Springer, Heidelberg (1991)

    Chapter  Google Scholar 

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Author information

Authors and Affiliations

  1. Institut für Informatik, Universität Leipzig, Augustusplatz 10-11, D-04109, Leipzig, Germany

    Ina Mäurer

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  1. Ina Mäurer
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Editor information

Editors and Affiliations

  1. LIF, CNRS & Univ. de Provence,, Marseille, France

    Bruno Durand

  2. RWTH Aachen University,, Lehrstuhl Informatik 7,, 52056,, Aachen,, Germany

    Wolfgang Thomas

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© 2006 Springer-Verlag Berlin Heidelberg

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Mäurer, I. (2006). Weighted Picture Automata and Weighted Logics. In: Durand, B., Thomas, W. (eds) STACS 2006. STACS 2006. Lecture Notes in Computer Science, vol 3884. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11672142_25

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  • DOI: https://doi.org/10.1007/11672142_25

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-32301-3

  • Online ISBN: 978-3-540-32288-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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