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Abstract

We study a quantitative model of traces, i.e. trace series which assign to every trace an element from a semiring. We show the coincidence of recognizable trace series with those which are definable by restricted formulas from a weighted logics over traces. We use a translation technique from formulas over words to those over traces, and vice versa. This way, we show also the equivalence of aperiodic and first-order definable trace series.

Keywords

Formal Power Series Atomic Formula Propositional Formula Trace Series Word Language 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Berstel, J., Reutenauer, C.: Rational Series and Their Languages. EATCS Monographs on Theoret. Comp. Sc., vol. 12. Springer, Heidelberg (1988)CrossRefMATHGoogle Scholar
  2. 2.
    Bollig, B.: On the expressiveness of asynchronous cellular automata. In: Liśkiewicz, M., Reischuk, R. (eds.) FCT 2005. LNCS, vol. 3623, pp. 528–539. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  3. 3.
    Bollig, B., Leucker, M.: Message-passing automata are expressively equivalent to EMSO logic. Theoret. Comp. Sc (to appear, 2006)Google Scholar
  4. 4.
    Büchi, J.R.: Weak second-order arithmetic and finite automata. Z. Math. Logik Grundlagen Math. (6), 66–92 (1960)Google Scholar
  5. 5.
    Diekert, V., Métivier, Y.: Partial commutation and traces. In: Rozenberg, G., Salomaa, A. (eds.) Handbook of Formal Languages, Beyond Words, ch. 8, vol. 3, pp. 457–534. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  6. 6.
    Diekert, V., Rozenberg, G. (eds.): The Book of Traces. World Scientific, Singapore (1995)Google Scholar
  7. 7.
    Droste, M., Gastin, P.: The Kleene-Schützenberger theorem for formal power series in partially commuting variables. Information and Computation 153, 47–80 (1999)MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Droste, M., Gastin, P.: On aperiodic and star-free formal power series in partially commuting variables. In: Formal Power Series and Algebraic Combinatorics (Moscow 2000), pp. 158–169. Springer, Berlin (2000)CrossRefGoogle Scholar
  9. 9.
    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)CrossRefGoogle Scholar
  10. 10.
    Droste, M., Vogler, H.: Weighted tree automata and weighted logics (submitted, 2005)Google Scholar
  11. 11.
    Ebinger, W., Muscholl, A.: Logical definability on infinite traces. Theoret. Comp. Sc. (154), 67–84 (1996)Google Scholar
  12. 12.
    C.C. Elgot. Decision problems of finite automata design and related arithmetics. Trans. Amer. Math. Soc., (98):21–52, 1961.Google Scholar
  13. 13.
    Golan, J.S.: Semirings and their Applications. Kluwer Academic Publishers, Dordrecht (1999)CrossRefMATHGoogle Scholar
  14. 14.
    Hebisch, U., Weinert, H.J.: Semirings: Algebraic Theory and Application. World Scientific, Singapore (1999)MATHGoogle Scholar
  15. 15.
    Kuich, W., Salomaa, A.: Semirings, Automata, Languages. EATCS Monographs on Theoret. Comp. Sc, vol. 5. Springer, Heidelberg (1986)CrossRefMATHGoogle Scholar
  16. 16.
    Kuske, D.: Weighted asynchronous cellular automata. In: Durand, B., Thomas, W. (eds.) STACS 2006. LNCS, vol. 3884, pp. 684–695. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  17. 17.
    Kuske, D., Meinecke, I.: Branching automata with costs – a way of reflecting parallelism in costs. Theoret. Comp. Sc. 328, 53–75 (2004)MathSciNetCrossRefMATHGoogle Scholar
  18. 18.
    Mäurer, I.: Weighted picture automata and weighted logics. In: Durand, B., Thomas, W. (eds.) STACS 2006. LNCS, vol. 3884, pp. 313–324. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  19. 19.
    Mazurkiewicz, A.: Trace theory. In: Brauer, W., Reisig, W., Rozenberg, G. (eds.) APN 1986. LNCS, vol. 255, pp. 279–324. Springer, Heidelberg (1987)Google Scholar
  20. 20.
    Meinecke, I.: Weighted Branching Automata – Combining Concurrency and Weights. Dissertation, Technische Universität Dresden, Germany (December 2004)Google Scholar
  21. 21.
    Meinecke, I.: The Hadamard product of sequential-parallel series. J. of Automata, Languages and Combinatorics 10(2) (toappear, 2005)Google Scholar
  22. 22.
    Salomaa, A., Soittola, M.: Automata-Theoretic Aspects of Formal Power Series. In: Texts and Monographs in Computer Science, Springer, Heidelberg (1978)Google Scholar
  23. 23.
    Schützenberger, M.P.: On the definition of a family of automata. Information and Control 4, 245–270 (1961)MathSciNetCrossRefMATHGoogle Scholar
  24. 24.
    Thomas, W.: On logical definability of trace languages. In: Diekert, V. (ed.) Proceedings of a workshop of the ESPRIT BRA No 3166: Algebraic and Syntactic Methods in Computer Science (ASMICS) 1989, Technical University of Munich, pp. 172–182 (1990)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Ingmar Meinecke
    • 1
  1. 1.Institut für InformatikUniversität LeipzigLeipzigGermany

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