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About fixpoints for concurrency

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Semantics of Systems of Concurrent Processes (LITP 1990)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 469))

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Abstract

This paper recalls some fixpoint theorems in ordered algebraic structures and surveys some ways in which these theorems are applied in computer science. It also points out the shortcomings of the classical least fixpoint theory for domains such as nondeterministic or parallel programs, and shows how to overcome these liabilities by introducing better and more refined fixpoint tools.

Support from the PRC Mathématiques-Informatique is gratefully acknowledged.

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5-References

  1. L. Aceto, M. Hennessy, Termination, deadlock and divergence, to appear in J. Assoc. Comput. Mach..

    Google Scholar 

  2. K. Apt, Efficient computing of least fixpoints, TR-88-33, Univ. Texas, Austin (1988).

    Google Scholar 

  3. K.R. Apt, H. Blair, A. Walker, Towards a theory of declarative knowledge, presented at the Workshop on Deductive data bases and logic programming, Washington D.C. (August 1986).

    Google Scholar 

  4. A. Arnold, M. Nivat, The metric space of infinite trees: Algebraic and Topological properties, Fund. Inform. 3 (1980), 445–476.

    Google Scholar 

  5. J. Bergstra, J. Klop, Algebra of communicating processes, Proc. CWI Symposium Mathematics and Computer Science, J. de Bakker, M. Hazenwinkel and J. Lenstra, eds. (1986).

    Google Scholar 

  6. G. Birkhoff, Lattice theory, 3rd edition, Americ. Math. Soc., New-York (1979).

    Google Scholar 

  7. M. Broy, On the Herbrand-Kleene universe for non deterministic computations, MFCS 84, LNCS 176, Springer-Verlag (1981), 214–222.

    Google Scholar 

  8. B. Courcelle, Arbres infinis et systèmes d'équations, RAIRO Info. Théor. 13 (1979), 31–48.

    Google Scholar 

  9. P. Darondeau, B. Gamatié, A fully observational model for infinite behaviors of communicating systems, to appear.

    Google Scholar 

  10. M.H. Van Emden, R.A. Kowalski, The Semantics of Predicate Logic as a Programming Language, Jour. Assoc. Comput. Mach. 23 (1976), 733–742.

    Google Scholar 

  11. H. Gallaire, J. Minker, J. M. Nicolas, Logic and data bases: a deductive approach, Assoc. Comput. Mach. Comput. Surveys, 16 (1984), 153–185.

    Google Scholar 

  12. J. Goguen, J. Thatcher, E. Wagner, J. Wright, Initial algebra semantics and continuous algebras, J. Assoc. Comput. Mach. 24 (1977), 68–95.

    Google Scholar 

  13. I. Guessarian, Algebraic Semantics, Lecture Notes in Comput. Sci. 99, Springer-Verlag, Berlin (1981).

    Google Scholar 

  14. I. Guessarian, A note on fixpoint techniques in data base recursive logic programs, RAIRO Info. Théor. 22 (1988), 49–56.

    Google Scholar 

  15. Improving fixpoint tools for computer science, IFIP'89 proceedings, G. Ritter ed., North-Holland (1989), 1109–1114.

    Google Scholar 

  16. E. Kranakis, Existence and uniqueness Theorems in fixed point semantics, CWI Report (1987).

    Google Scholar 

  17. S. Kraus, D. Lehmann, M. Magidor, Preferential models and cumulative logics, Submitted.

    Google Scholar 

  18. J.-L. Lassez, V.L. Nguyen, E.A. Sonenberg, Fixed point theorems and semantics a folk tale, Inform. Proces. Letters 14 (1982), 112–116.

    Google Scholar 

  19. D. Makinson, General theory of cumulative inference, unpublished manuscript.

    Google Scholar 

  20. R. Milner, A Calculus of Communicating systems, LNCS 92, Springer Verlag (1980).

    Google Scholar 

  21. M. Nivat, On the interpretation of recursive polyadic program schemes, Symp. Math. 15, Rome (1975), 255–281.

    Google Scholar 

  22. W. Rounds, Applications of topology to semantics of communicating processes, LNCS, 197, Springer Verlag (1985), 360–372.

    Google Scholar 

  23. W. Rounds, On the relationships between Scott domains, synchronization trees, and metric spaces, Inf. and Control 66 (1985), 6–28.

    Google Scholar 

  24. D. Scott, The lattice of flowdiagrams, Symp. on Semantics of Algorithmic Languages, Lect. Notes Math. 188, Springer Verlag, Berlin (1971), 311–366.

    Google Scholar 

  25. J. Tiuryn, Unique fixed points vs. least fixed points, Theor. Comput. Sci. 12 (1980), 229–254.

    Google Scholar 

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Authors and Affiliations

  1. 2, Place Jussieu, 75252, Paris Cedex 05, France

    Irène Guessarian

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  1. Irène Guessarian
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Irène Guessarian

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© 1990 Springer-Verlag

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Guessarian, I. (1990). About fixpoints for concurrency. In: Guessarian, I. (eds) Semantics of Systems of Concurrent Processes. LITP 1990. Lecture Notes in Computer Science, vol 469. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-53479-2_15

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  • DOI: https://doi.org/10.1007/3-540-53479-2_15

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-53479-2

  • Online ISBN: 978-3-540-46897-4

  • eBook Packages: Springer Book Archive

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