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An algebraic characterisation of elementary net system (observable) state space

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Formal Aspects of Computing

Abstract

The paper proposes a characterisation of the state space ofan Elementary Net (EN) system in terms of a relational algebraic structure, called Local State Transformation (LST) algebra. The latter allows one to take into consideration in an explicit way local state transformations performed by the occurrence of events. A class of injective morphisms between LST algebras allows one to compare system behaviours at different levels of abstraction and to introduce a notion of preorder in the class of EN systems. This leads in a natural way to a notion of equivalence which preserves the system degree of concurrency, and whose equivalence classes have a unique (up to isomorphism) canonical representative which is minimal with respect to net elements. Moreover, the class of morphisms allows the definition of a notion of state observability and of a notion of equivalence between Observable Elementary Net Systems. All these notions provide the system designer with a set of useful tools for an incremental design process, in which the (concurrent and nondeterministic) control of the considered system need not be fixed ‘a priori’.

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Authors and Affiliations

  1. Dipartimento di Scienze dell’Informazione, via Comelico 39, 20135, Milano, Italy

    L. Pomello & C. Simone

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  1. L. Pomello
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  2. C. Simone
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Accepted in revised form October 1991 by E. Astesiano

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Pomello, L., Simone, C. An algebraic characterisation of elementary net system (observable) state space. Formal Aspects of Computing 4 (Suppl 1), 612–637 (1992). https://doi.org/10.1007/BF03180565

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  • DOI: https://doi.org/10.1007/BF03180565

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