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Omega Algebra, Demonic Refinement Algebra and Commands

  • Peter Höfner
  • Bernhard Möller
  • Kim Solin
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4136)

Abstract

Weak omega algebra and demonic refinement algebra are two ways of describing systems with finite and infinite iteration. We show that these independently introduced kinds of algebras can actually be defined in terms of each other. By defining modal operators on the underlying weak semiring, that result directly gives a demonic refinement algebra of commands. This yields models in which extensionality does not hold. Since in predicate-transformer models extensionality always holds, this means that the axioms of demonic refinement algebra do not characterise predicate-transformer models uniquely. The omega and the demonic refinement algebra of commands both utilise the convergence operator that is analogous to the halting predicate of modal μ-calculus. We show that the convergence operator can be defined explicitly in terms of infinite iteration and domain if and only if domain coinduction for infinite iteration holds.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Peter Höfner
    • 1
  • Bernhard Möller
    • 1
  • Kim Solin
    • 1
    • 2
  1. 1.Institut für InformatikUniversität AugsburgAugsburgGermany
  2. 2.Turku Centre for Computer ScienceÅboFinland

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