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Relating multifunctions and predicate transformers through closure operators

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Theoretical Aspects of Computer Software (TACS 1994)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 789))

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Abstract

We study relations between predicate transformers and multifunctions in a topological setting based on closure operators. We give topological definitions of safety and liveness predicates and using these predicates we define predicate transformers. State transformers are multifunctions with values in the collection of fixed points of a closure operator. We derive several isomorphisms between predicate transformers and multifunctions. By choosing different closure operators we obtain multifunctions based on the usual power set construction, on the Hoare, Smyth and Plotkin power domains, and based on the compact and closed metric power constructions. Moreover, they are all related by isomorphisms to the predicate transformers.

The research of this author was partially supported by a grant of the Centro Nazionale delle Ricerche (CNR), Italy, announcement no. 203.15.3 of 15/2/90.

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Author information

Authors and Affiliations

  1. Department of Computer Science, Vrije Universiteit Amsterdam, De Boelelaan 1081a, 1081, HV Amsterdam, The Netherlands

    Marcello M. Bonsangue

  2. Department of Computer Science, Utrecht University, P.O. Box 80.089, 3508, TB Utrecht, The Netherlands

    Joost N. Kok

Authors
  1. Marcello M. Bonsangue
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  2. Joost N. Kok
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Masami Hagiya John C. Mitchell

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© 1994 Springer-Verlag Berlin Heidelberg

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Bonsangue, M.M., Kok, J.N. (1994). Relating multifunctions and predicate transformers through closure operators. In: Hagiya, M., Mitchell, J.C. (eds) Theoretical Aspects of Computer Software. TACS 1994. Lecture Notes in Computer Science, vol 789. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57887-0_127

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  • DOI: https://doi.org/10.1007/3-540-57887-0_127

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