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Series and Parallel Operations on Pomsets

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Foundations of Software Technology and Theoretical Computer Science (FSTTCS 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1738))

Abstract

We consider two-sorted algebras of pomsets (isomorphism classes of labeled partial orders) equipped with the operations of series and parallel product and series and parallel omega power. The main results show that these algebras possess a non-finitely based polynomial time decidable equational theory, which can be axiomatized by an infinite set of simple equations. Alongthe way of provingthe se results, we show that the free algebras in the corresponding variety can be described by generalized series-parallel pomsets. We also provide a graph theoretic characterization of the generalized series-parallel pomsets.

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References

  1. L. Aceto. Full abstraction for series-parallel pomsets. In: TAPSOFT 91, LNCS 493, 1–25, Springer-Verlag, 1991. 316, 317

    Google Scholar 

  2. Ch. Baier and M. E. Majster-Cederbaum. Denotational semantics in the cpo and metric approach. Theoret. Comput. Sci., 135:171–220, 1994. 316

    Article  MATH  MathSciNet  Google Scholar 

  3. S. L. Bloom and Z. Ésik. Free shuffle algebras in language varieties. Theoret. Comput. Sci., 163:55–98, 1996. 316, 317, 317, 317

    Article  MATH  MathSciNet  Google Scholar 

  4. S. L. Bloom and Z. Ésik. Shuffle binoids. Theoret. Inform. Appl., 32:175–198, 1998. 316, 317, 317, 319, 319, 321

    Google Scholar 

  5. G. Boudol and I. Castellani. Concurrency and atomicity. Theoret. Comput. Sci., 59:1988, 25–84. 316, 316, 317, 317

    Article  MATH  MathSciNet  Google Scholar 

  6. B. Bloom and M. Kwiatkowska. Trade-offs in true concurrency: Pomsets and Mazurkiewicz traces. In: MFPS 91, LNCS 598, 350–375, Springer-Verlag, 1992. 316, 317

    Google Scholar 

  7. J. W. de Bakker and J. H. A. Warmerdam. Metric pomset semantics for a concurrent language with recursion. In: Semantics of Systems of Concurrent Processes, LNCS 469, 21–49, Springer-Verlag, 1990. 316, 317

    Google Scholar 

  8. J. L. Gischer. The equational theory of pomsets. Theoret. Comput. Sci., 61:199–224, 1988. 316, 317

    Article  MATH  MathSciNet  Google Scholar 

  9. J. Grabowski. On partial languages. Fund. Inform., 4:427–498, 1981. 316, 316, 317, 317, 317, 319, 321

    MATH  MathSciNet  Google Scholar 

  10. L. Kucera. Combinatorial Algorithms. Adam Hilger, Bristol and Philadelphia, 1990. 326

    MATH  Google Scholar 

  11. K. Lodaya and P. Weil. Series-parallel posets: algebra, automata and languages. In: STACS 98, LNCS 1373, 555–565, Springer-Verlag, 1998. 316

    Chapter  Google Scholar 

  12. A. Mazurkiewicz. Concurrency, modularity and synchronization. In: MFCS 89, LNCS 379, 577–598, Springer-Verlag, 1989. 316

    Google Scholar 

  13. J.-J. Ch. Meyer and E. P. de Vink. Pomset semantics for true concurrency with synchronization and recursion. In: MFCS 89, LNCS 379, 360–369, 1989. 316

    Google Scholar 

  14. V. Pratt. Modelingcon currency with partial orders. Internat. J. Parallel Processing, 15:33–71, 1986. 316, 317, 318

    Article  MATH  MathSciNet  Google Scholar 

  15. A. Rensink. Algebra and theory of order-deterministic pomsets. Notre Dam J. Formal Logic, 37:283–320, 1996. 316, 317

    Article  MATH  MathSciNet  Google Scholar 

  16. S. T. Tschantz. Languages under concatenation and shuffling. Math. Structures Comput. Sci., 4:505–511, 1994. 316, 317

    Article  MATH  MathSciNet  Google Scholar 

  17. J. Valdes, R. E. Tarjan, and E. L. Lawler. The recognition of series-parallel digraphs. SIAM Journal of Computing, 11(2):298–313, 1982. 316, 317, 321

    Article  MATH  MathSciNet  Google Scholar 

  18. Th. Wilke. An Eilenbergt heorem for ∞-languages. In: ICALP 91, LNCS 510, 588–599, 1991. 327

    Google Scholar 

  19. H. Wimmel and L. Priese. Algebraic characterization of Petri net pomset semantics. In: CONCUR 97, LNCS 1243, 406–420, Springer-Verlag, 1997. 316

    Google Scholar 

  20. J. Winkowski. Behaviours of concurrent systems. Theoret. Comput. Sci., 12:39–60, 1980. 316

    Article  MATH  MathSciNet  Google Scholar 

  21. I. Winkowski. Concatenable weighted pomsets and their applications to modelling processes of Petri nets. Fund. Inform., 28:403–421, 1996. 316

    MATH  MathSciNet  Google Scholar 

  22. G. Winskel. Event structures. In: Petri Nets: Applications and Relationships to Other Models of Concurrency, Advances in Petri Nets 1986, Part II, Proceedings of an Advanced Course, LNCS 255, 325–392, Springer-Verlag, 1987. 316

    Google Scholar 

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Author information

Authors and Affiliations

  1. Dept. of Computer Science, A. József University, Aradi v. tere 1., 6720, Szeged, Hungary

    Zoltán Ésik

  2. Department of Computer Software, The University of Aizu, Aizu-Wakamatsu-City, Fukushima, 965-8580, Japan

    Satoshi Okawa

Authors
  1. Zoltán Ésik
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  2. Satoshi Okawa
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Engineering, Indian Institute of Technology, Chennai, 600036, India

    C. Pandu Rangan

  2. Institute of Mathematical Sciences C.I.T. Campus, Chennai, 600113, India

    V. Raman  & R. Ramanujam  & 

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© 1999 Springer-Verlag Berlin Heidelberg

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Ésik, Z., Okawa, S. (1999). Series and Parallel Operations on Pomsets. In: Rangan, C.P., Raman, V., Ramanujam, R. (eds) Foundations of Software Technology and Theoretical Computer Science. FSTTCS 1999. Lecture Notes in Computer Science, vol 1738. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46691-6_25

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  • DOI: https://doi.org/10.1007/3-540-46691-6_25

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66836-7

  • Online ISBN: 978-3-540-46691-8

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