A state transformation preorder over a class of EN systems

The paper introduces a notion of preorder between Elementary Net Systems which is based on the observability of places. This latter allows one to define the notion of Observable Local States whose transformations are the main concern of the proposed preorder, called State Transformation (ST) preorder. ST preorder compares systems with a different level of granularity in local states transformation by requiring an injective morphism between their algebraic structures of observable local states. In addition, it allows one to define in a standard way a notion of ST equivalence. This latter is related to a previous notion, EF equivalence, for which the existence of canonical representatives has been previously proved. Finally, ST preorder and equivalence over a subclass of EN systems (the S-observable systems) are discussed in the framework of system development.

[1]  Lucia Pomello,et al.  Refinement of Concurrent Systems Based on Local State Transformations , 1989, REX Workshop.

[2]  Wilfried Brauer,et al.  Net Theory and Applications , 1980, Lecture Notes in Computer Science.

[3]  Samson Abramsky,et al.  Observation Equivalence as a Testing Equivalence , 1987, Theor. Comput. Sci..

[4]  Robert Valette,et al.  Analysis of Petri Nets by Stepwise Refinements , 1979, J. Comput. Syst. Sci..

[5]  Lucia Pomello,et al.  Some equivalence notions for concurrent systems. An overview , 1985, Applications and Theory in Petri Nets.

[6]  Giorgio De Michelis,et al.  GAMERU: A language for the analysis and design of human communication pragmatics within organizational systems , 1986, European Workshop on Applications and Theory of Petri Nets.

[7]  Rocco De Nicola,et al.  Observational equivalences for concurrency models , 1987, Formal Description of Programming Concepts.

[8]  Grzegorz Rozenberg,et al.  Advances in Petri Nets 1985 , 1985, Lecture Notes in Computer Science.

[9]  P. S. Thiagarajan.  Elementary Net Systems , 1986 .

[10]  Giorgio De Michelis,et al.  Exhibited-Behaviour Equivalence and Organizational Abstraction in Concurrent System Design , 1985, ICDCS.

[11]  Grzegorz Rozenberg,et al.  Concurrency and Nets , 1987, Springer Berlin Heidelberg.

[12]  K. Voss,et al.  Interface as a basic concept for systems specification and verification , 1987 .

[13]  Gérard Berthelot,et al.  Checking properties of nets using transformation , 1985, Applications and Theory in Petri Nets.

[14]  Wolfgang Reisig,et al.  Petri Nets: Central Models and Their Properties , 1986, Lecture Notes in Computer Science.

[15]  Giorgio De Michelis,et al.  A State Transformation Equivalence for Concurrent Systems: Exhibited Functionality-equivalence , 1988, Concurrency.