Replacement of open interface subnets and stable state transformation equivalence

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 N ₁ ≡_SST N ₂ and N ₂ is robust (robust OI-nets are a subclass of OI-nets) then N [N ₁ ← N₂] ≡sf N. 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-}$}}{ \prec } _{SF}^{ - 1} = \equiv _{SF}$.

This work is part of BULL's contribution to DEMON (ESPRIT BRA 3148)