Polynomials, Fragments of Temporal Logic and the Variety DA over Traces

  • Manfred Kufleitner
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4036)


We show that some language theoretic and logical characterizations of recognizable word languages whose syntactic monoid is in the variety DA also hold over traces. To this aim we give algebraic characterizations for the language operations of generating the polynomial closure and generating the unambiguous polynomial closure over traces.

We also show that there exist natural fragments of local temporal logic that describe this class of languages corresponding to DA. All characterizations are known to hold for words.


Temporal Logic Language Variety Semigroup Variety Commutative Monoids Algebraic Characterization 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Diekert, V., Rozenberg, G. (eds.): The Book of Traces. World Scientific, Singapore (1995)Google Scholar
  2. 2.
    Eilenberg, S.: Automata, Languages, and Machines, vol. B. Academic Press, New York, London (1976)MATHGoogle Scholar
  3. 3.
    Gastin, P., Mukund, M.: An elementary expressively complete temporal logic for Mazurkiewicz traces. In: Widmayer, P., Triguero, F., Morales, R., Hennessy, M., Eidenbenz, S., Conejo, R. (eds.) ICALP 2002. LNCS, vol. 2380, pp. 938–949. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  4. 4.
    Mazurkiewicz, A.: Concurrent program schemes and their interpretations. DAIMI Rep. PB, vol. 78. Aarhus University, Aarhus (1977)Google Scholar
  5. 5.
    Ochmański, E.: Recognizable trace languages. In: Diekert, V., Rozenberg, G. (eds.) The Book of Traces, ch. 6, pp. 167–204. World Scientific, Singapore (1995)CrossRefGoogle Scholar
  6. 6.
    Pin, J.-É.: Varieties of Formal Languages. North Oxford Academic, London (1986)MATHGoogle Scholar
  7. 7.
    Pin, J.-É.: A variety theorem without complementation. Russian Mathematics (Izvestija vuzov.Matematika) 39, 80–90 (1995)MathSciNetGoogle Scholar
  8. 8.
    Pin, J.-É., Straubing, H., Thérien, D.: Locally trivial categories and unambiguous concatenation. Journal of Pure and Applied Algebra 52, 297–311 (1988)MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Pin, J.-É., Weil, P.: Profinite semigroups, Mal’cev products and identities. Journal of Algebra 182, 604–626 (1996)MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Pin, J.-É., Weil, P.: Polynominal closure and unambiguous product. Theory Comput. Syst. 30(4), 383–422 (1997)MATHMathSciNetGoogle Scholar
  11. 11.
    Tesson, P.: Personal communicationGoogle Scholar
  12. 12.
    Tesson, P., Thérien, D.: Diamonds are Forever: The Variety DA. In: dos Gomes Moreira da Cunha, G.M., da Silva, P.V.A., Pin, J.-E. (eds.) Semigroups, Algorithms, Automata and Languages, Coimbra (Portugal) 2001, pp. 475–500. World Scientific, Singapore (2002)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Manfred Kufleitner
    • 1
  1. 1.Universität Stuttgart, FMIGermany

Personalised recommendations