Object Petri Nets: Definitions, Properties, and Related Models

In this presentation the decidability issues of formalisms that allow Petri nets as tokens are studied. Especially for "elementary object-net systems" defined by Valk the decidability of the reachability and the boundedness problem is considered. It is shown that reachability becomes undecidable while boundedness remains decidable for elementary object-net systems. Furthermore it is shown that even for minimal extensions the formalism obtains the power of Turing machines.

[1]  Luca Cardelli,et al.  Mobility Types for Mobile Ambients , 1999, ICALP.

[2]  Philippe Schnoebelen,et al.  Some Decidability Results for Nested Petri Nets , 1999, Ershov Memorial Conference.

[3]  Rüdiger Valk,et al.  Petri Nets as Token Objects: An Introduction to Elementary Object Nets , 1998, ICATPN.

[4]  Hartmut Ehrig,et al.  Fundamentals of Algebraic Specification 1 , 1985, EATCS Monographs on Theoretical Computer Science.

[5]  Gul Agha,et al.  Concurrent Object-Oriented Programming and Petri Nets , 2001, Lecture Notes in Computer Science.

[6]  Richard M. Karp,et al.  Parallel Program Schemata , 1969, J. Comput. Syst. Sci..

[7]  Luca Cardelli,et al.  Ambient Groups and Mobility Types , 2000, IFIP TCS.

[8]  Undecidability in Object-Oriented Petri Nets , 2000 .

[9]  Berndt Farwer,et al.  Mobile Object-Net Systems and their Processes , 2003, Fundam. Informaticae.

[10]  Irina A. Lomazova,et al.  Nested Petri Nets - a Formalism for Specification and Verification of Multi-Agent Distributed Systems , 2000, Fundam. Informaticae.

[11]  Jeffrey D. Ullman,et al.  Introduction to Automata Theory, Languages and Computation , 1979 .

[12]  Wolfgang Reisig,et al.  Petri Nets and Algebraic Specifications , 1991, Theor. Comput. Sci..

[13]  Philippe Schnoebelen,et al.  Reset Nets Between Decidability and Undecidability , 1998, ICALP.

[14]  Heiko Rölke,et al.  Concurrency in Mobile Object Net Systems , 2003, Fundam. Informaticae.

[15]  Mogens Nielsen,et al.  Decidability Issues for Petri Nets - a survey , 1994, Bull. EATCS.

[16]  Narciso Martí-Oliet,et al.  Maude: specification and programming in rewriting logic , 2002, Theor. Comput. Sci..

[17]  Gianfranco Ciardo,et al.  Petri Nets with Marking-Dependent Ar Cardinality: Properties and Analysis , 1994, Application and Theory of Petri Nets.

[18]  Ernst W. Mayr.  An Algorithm for the General Petri Net Reachability Problem , 1984, SIAM J. Comput..

[19]  Berndt Farwer.  A Linear Logic View of Object Petri Nets , 1999, Fundam. Informaticae.

[20]  Rüdiger Valk.  Self-Modifying Nets, a Natural Extension of Petri Nets , 1978, ICALP.

[21]  José Meseguer,et al.  Specification and proof in membership equational logic , 2000, Theor. Comput. Sci..

[22]  Daniel Moldt,et al.  Modelling Mobility and Mobile Agents Using Nets within Nets , 2003, ICATPN.

[23]  Tadao Kasami,et al.  Some Decision Problems Related to the Reachability Problem for Petri Nets , 1976, Theor. Comput. Sci..

[24]  Philippe Schnoebelen,et al.  Well-structured transition systems everywhere! , 2001, Theor. Comput. Sci..

[25]  Peter Csaba Ölveczky,et al.  Rewriting Logic as a Unifying Framework for Petri Nets , 2001, Unifying Petri Nets.

[26]  José Meseguer,et al.  Petri Nets Are Monoids , 1990, Inf. Comput..

[27]  MeseguerJosé.  Conditional rewriting logic as a unified model of concurrency , 1992 .