The Limit of Splitn-Language Equivalence

Splitting is a simple form of action refinement that may be used to express the duration of actions. In particular,splitnsubdivides each action intonphases. Petri netsNandN? aresplitn-language equivalent ifsplitn(N) andsplitn(N?) are language equivalent. It is known that these equivalences get finer and finer with increasingn. This paper characterizes the limit of this sequence by a newly defined partial order semantics. This semantics is obtained from the interval-semiword semantics, which is fully abstract for action refinement and language equivalence, by closing it under a special swap operation. The new swap equivalence lies strictly between interval-semiword and step-sequence equivalence.

[1]  Matthew Hennessy,et al.  Axiomatising Finite Concurrent Processes , 1988, SIAM J. Comput..

[2]  Walter Vogler,et al.  The Limit of Split_n-Language Equivalence , 1995, ICALP.

[3]  Raymond R. Devillers.  Maximality preservation and the ST-idea for action refinements , 1992, Advances in Petri Nets: The DEMON Project.

[4]  Walter Vogler,et al.  Modular Construction and Partial Order Semantics of Petri Nets , 1992, Lecture Notes in Computer Science.

[5]  Walter Vogler,et al.  Timed Testing of Concurrent Systems , 1993, Inf. Comput..

[6]  Rob J. van Glabbeek.  The Refinement Theorem for ST-bisimulation Semantics , 1990, Programming Concepts and Methods.

[7]  J. Grabowski,et al.  On partial languages , 1981, Fundam. Informaticae.

[8]  Eike Best,et al.  Nonsequential Processes: A Petri Net View , 1988 .

[9]  Wolfgang Reisig,et al.  The Non-sequential Behavior of Petri Nets , 1983, Inf. Control..

[10]  Volker Diekert,et al.  Combinatorics on Traces , 1990, Lecture Notes in Computer Science.

[11]  Luca Aceto,et al.  Towards Action-Refinement in Process Algebras , 1993, Inf. Comput..

[12]  Astrid Kiehn.  On the Interrelation Between Synchronized and Non-Synchronized Behaviour of Petri Nets , 1988, J. Inf. Process. Cybern..

[13]  Cosimo Laneve,et al.  Split and ST Bisimulation Semantics , 1995, Inf. Comput..

[14]  Peter H. Starke,et al.  Processes in Petri Nets , 1981, J. Inf. Process. Cybern..

[15]  Ursula Goltz,et al.  Equivalence Notions for Concurrent Systems and Refinement of Actions (Extended Abstract) , 1989, MFCS.

[16]  Albert R. Meyer,et al.  Testing Equivalence for Petri Nets with Action Refinement: Preliminary Report , 1992, CONCUR.

[17]  Ursula Goltz,et al.  Parial order semantics for refinement of actions - neither necessary nor always sufficient but appropriate when used with care , 1989, Bull. EATCS.

[18]  Frits W. Vaandrager,et al.  The Difference between Splitting in n and n+1 , 1995, Inf. Comput..

[19]  Arend Rensink.  Models and Methods for Action Refinement , 1993 .

[20]  Walter Vogler.  Bisimulation and Action Refinement , 1993, Theor. Comput. Sci..

[21]  Roberto Gorrieri,et al.  A Causal Operational Semantics of Action Refinement , 1995, Inf. Comput..

[22]  Cosimo Laneve,et al.  The Limit of Split_n-Bisimulations for CCS Agents , 1991, International Symposium on Mathematical Foundations of Computer Science.

[23]  Maciej Koutny,et al.  Representations of Discrete Interval Orders and Semi-Orders , 1994, J. Inf. Process. Cybern..