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Poset properties of complex traces

  • Paul Gastin
  • Antoine Petit
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 629)

Abstract

This paper investigates PoSct properties of the monoid ℂ of infinite dependence graphs and of the monoid ℂ of complex traces. We show that a subset of G admits a least upper bound if and only if this set is coherent and countable. Hence, G is bounded complete. The compact and the prime graphs in G arc characterized and we prove that each graph is the least upper bound of its compact (resp. its prime) lower bounds. Therefore, up to the restriction to countable sets, G is a coherently complete Scott-Domain and is Prime Algebraic. We define very naturally two orders on ℂ: the product order and the prefix order. We show that ℂ with each order is a coherently complete CPO and we characterize the least upper bound (the greatest lower bound resp.) of a subset of ℂ when it exists. But contrary to the case of G, we prove that ℂ is not a Scott-Domain in general.

Keywords

Partial Order Dependence Graph Prime Graph Product Order Real Trace 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • Paul Gastin
    • 1
  • Antoine Petit
    • 2
  1. 1.LITP, Institut Blaise PascalUniversité Paris 6Paris Cedex 05France
  2. 2.LRI, URA CNRS 410Université Paris SudOrsay CedexFrance

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