An algebraic characterisation of elementary net system (observable) state space
Lucia Pomello, C. Simoné · Formal Aspects of Computing · 1992
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’.