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Using least fixed points to characterize formal computations of non-deterministic equations

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Formalization of Programming Concepts (ICFPC 1981)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 107))

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Abstract

We extend the least fixed point techniques to the case of non-deterministic equations. Commutative idempotent semigroups in the category of ω-complete posets are used as non-deterministic domains.

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References

  1. ADJ-group: A junction between computer science and category theory. IBM research report RC-4526, 1973

    Google Scholar 

  2. ADJ-group: Some fundamentals of order algebraic semantics. MFCS '76, Lect. Notes in Comp. Sci. 45, 1976

    Google Scholar 

  3. ADJ-group: Rational algebraic theories and fixed-point solutions. 17th IEEE Symp. on Found. of Comp., Houston 1976

    Google Scholar 

  4. ADJ-group: Programming languages as mathematical objects. MFCS '78, Lect. Notes in Comp. Sci. 64, 1978

    Google Scholar 

  5. A.Arnold, M.Nivat: Non deterministic recursive program schemes. FCT '77, Lect. Notes in Comp. Sci. 56, Poznan 1977

    Google Scholar 

  6. A.Arnold, M.Nivat: Metric interpretations of infinite trees and semantics of non deterministic programs. Techn. Rep., Lille 1978

    Google Scholar 

  7. A.Arnold, M.Nivat: Formal computations of non deterministic recursive program schemes. Math. Syst. Th. 13, 1980

    Google Scholar 

  8. J.Engelfriet, E.M.Schmidt: IO and OI, JCSS 15, 1977

    Google Scholar 

  9. M.C.B.Hennessy, G.Plotkin: Full abstraction of a simple programming language. MFCS '79, Lect. Notes in Comp. Sci. 74, 1979

    Google Scholar 

  10. H.Huwig, A.Poigné: Continuous and non-deterministic completions of algebras. 3rd Hungarian Computer Science Conf., Budapest 1981

    Google Scholar 

  11. S.MacLane: Kategorien. Berlin-Heidelberg-New-York 1972

    Google Scholar 

  12. T.S.E.Maibaum: The semantics of non-determinism. Res. rep. CS-77-30, Waterloo 1977

    Google Scholar 

  13. E.G.Manes: Algebraic theories. Berlin-Heidelberg-New-York 1976

    Google Scholar 

  14. J.Meseguer: On order-complete universal algebra and enriched functorial semantics. FCT '77, Lect. Notes in Comp. Sci. 56, Poznan 1977

    Google Scholar 

  15. G. Plotkin: A power domain construction. SIAM Journ. on Comp. 5, 1976

    Google Scholar 

  16. A.Poigné: A least fixpoint approach to systems of non-deterministic equations. 3rd works. Categorical and alg. methods in Comp. Sci., Techn. rep., Dortmund 1980

    Google Scholar 

  17. A.Poigné: A least fixed point semantics of non-deterministic schemes. forthcoming

    Google Scholar 

  18. M.B.Smyth: Power domains. JCSS 16, 1978

    Google Scholar 

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Authors and Affiliations

  1. Informatik II, Universität Dortmund, Postfach 500 500, D-4600, Dortmund 50

    Axel Poigné

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  1. Axel Poigné
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Editor information

J. Díaz I. Ramos

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© 1981 Springer-Verlag Berlin Heidelberg

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Poigné, A. (1981). Using least fixed points to characterize formal computations of non-deterministic equations. In: Díaz, J., Ramos, I. (eds) Formalization of Programming Concepts. ICFPC 1981. Lecture Notes in Computer Science, vol 107. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-10699-5_118

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  • DOI: https://doi.org/10.1007/3-540-10699-5_118

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10699-9

  • Online ISBN: 978-3-540-38654-4

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