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Replacement of open interface subnets and stable state transformation equivalence

  • Ghassan Chehaibar
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 674)

Abstract

The aim of this paper is to provide a hierarchical design method, refinement by replacing place-bordered subnets, with a hierarchical analysis method based on equivalence and preorder. We consider nets with distinguised places (interface places) and distinguished states (stable states), called open interface nets (OI-nets); OI-systems are OI-nets such that the stable state set is a home space. Two equivalence notions are defined: ≡SF on OI-systems and ≡SST on OI-nets. We show that if N1SSTN2 and N2 is robust (robust OI-nets are a subclass of OI-nets) then N [N1 ← N2] ≡sfN. Since an equivalence is too restrictive in hierarchical design and it is only possible to replace subnets of N whose border is a subset of the interface of N, an interface expansion operation is defined giving rise to a preorder \(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{ \prec } _{SF}\) such that \(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{ \prec } _{SF} \cap \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{ \prec } _{SF}^{ - 1} = \equiv _{SF}\).

Key words

Place-Transition Nets Hierarchical Design and Analysis Open Interface Nets and Systems Stable State Transformation Equivalence and Preorder Replacement Expansion Robust Open Interface Nets 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Ghassan Chehaibar
    • 1
    • 2
  1. 1.BULL Corporate Research CenterBldg F3.2G.28 Rue Jean JaurèsLes Clayes-Sous-BoisFrance
  2. 2.Laboratory MASIUniversity Paris 6, Tower 65Paris Cedex 05France

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