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A theory of nondeterminism

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Automata, Languages and Programming (ICALP 1980)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 85))

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Abstract

A construction is described which takes an arbitrary set of machines, an arbitray set of tests, and an arbitrary relation on machines and tests defining which machines pass which tests. It produces a domain of specifications, which is a retract of the lattice of sets of tests (with the subset ordering), and a domain of nondeterministic machines (ndms), which is a retract of the lattice of sets of machines (with the superset ordering). These two domains are isomorphic. Simple conditions ensure that they are ω-algebraic.

Functions on such domains may be defined equivalently either as transformations of ndms (an operational definition) or as transformations of specifications (an axiomatic definition). Conditions for the "realism" of such functions are formulated.

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References

  1. Bell, J.L. and Slomson, A.B., "Models and ultraproducts" (North-Holland, 1969).

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  3. Scott, D., "Data types as lattices", SIAM J. Computing 5, 522–587 (1976).

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Author information

Authors and Affiliations

  1. Department of Computer Science, Edinburgh University, UK

    J. R. Kennaway

  2. Programming Research Group, Oxford University, UK

    C. A. R. Hoare

Authors
  1. J. R. Kennaway
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  2. C. A. R. Hoare
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Editor information

Jaco de Bakker Jan van Leeuwen

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© 1980 Springer-Verlag Berlin Heidelberg

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Kennaway, J.R., Hoare, C.A.R. (1980). A theory of nondeterminism. In: de Bakker, J., van Leeuwen, J. (eds) Automata, Languages and Programming. ICALP 1980. Lecture Notes in Computer Science, vol 85. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-10003-2_82

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  • DOI: https://doi.org/10.1007/3-540-10003-2_82

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10003-4

  • Online ISBN: 978-3-540-39346-7

  • eBook Packages: Springer Book Archive

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