On the Spatial Boundedness of Cellular RDA-nets
https://doi.org/10.18255/1818-1015-2017-4-391-409
Abstract
Cellular resource driven automata nets (CRDA-nets) is a generalization of the concept of two-level resource nets (Petri nets) with an infinite regular system grid. This formalism is a hybrid of Petri nets and asynchronous Cellular Automata and is designed for modeling multi-agent systems with dynamic spatial structure. Spatial boundedness is a property that guarantees the preservation of the finiteness of “geometric dimensions” of the active part of the system (for example, the living space) during its lifetime. Three variants of spatial boundedness for cellular RDA-nets are defined: localization, bounded diameter and bounded area. The properties of the corresponding algorithmic problems are investigated, their undecidability in the general case is proved. A non-trivial criterion for the localization of an one-dimensional CRDA-net is proposed, based on the new concept of the RDA propagation graph. An algorithm is described for constructing a propagation graph, using the method of saturation of generating paths. A method for estimating the diameter of an 1-dim CRDA with a bounded propagation graph is presented.
References
1. Bashkin V.A., “Nets of active resources”, Model. Anal. Inform. Sist., 14:4 (2007), 13-19, (in Russian).
2. Bashkin V. A., “Formalization of semantics of systems with unreliable agents by means of nets of active resources”, Progr. and Comp. Soft., 36:4 (2010), 187-196
3. Zaitsev D. A., “Verification of computing grids with special edge conditions by infinite Petri nets”, Automatic Control and Computer Sciences, 47:7 (2013), 403-412
4. Kotov V. E., Seti Petri, Nauka, Moskva, 2008, (in Russian)
5. Kuzmin E. V., Chalyy D. Ju., “On the decidability of boundedness problems for counter Minsky machines”, Model. Anal. Inform. Sist., 15:1 (2008), 16-26. (in Russian).
6. Alur R., Dill D., “Automata for modeling real-time systems” (Automata, Languages and Programming), Lecture Notes In Computer Science, 443 (1990), 322-335.
7. Bashkin V. A., “Nets of active resources for distributed systems modeling”, Joint Bulletin of NCC&IIS, Comp. Science, 28 (2008), 43-54.
8. Bashkin V. A., Lomazova I. A., “Resource Driven Automata Nets”, Fundamenta Informaticae, 109:3 (2011), 223-236.
9. Bashkin V. A., Lomazova I. A., “Cellular Resource Driven Automata Nets”, Fundamenta Informaticae, 120:3-4 (2012), 245-259.
10. Bashkin V. A., Lomazova I. A., Novikova Yu. A., “Timed Resource Driven Automata Nets for Distributed Real-Time Systems Modelling” (Parallel Computing Technologies), Lecture Notes In Computer Science, 7979 (2013), 13-25.
11. Bednarczyk M. A., Bernardinello L., Pawlowski W., Pomello L., “Modelling mobility with Petri Hypernets” (Recent Trends in Algebraic Development Techniques), Lecture Notes In Computer Science, 3423 (2005), 28-44.
12. Cook M., “Universality in Elementary Cellular Automata.”, Complex Systems, 15:1 (2004), 1-40.
13. Finkel A., Schnoebelen Ph., “Well-Structured Transition Systems Everywhere!”, Theoretical Computer Science, 256:1-2 (2001), 63-92.
14. Jensen K., Colored Petri Nets: Basic Concepts, Analysis Methods and Practical Use, Springer, 1994.
15. K¨ohler-Bußmeier M., “Hornets: Nets within Nets combined with Net Algebra” (ICATPN’2009), Lecture Notes In Computer Science, 5606 (2009), 243-262.
16. Lomazova I. A., “Nested Petri Nets - a Formalism for Specification and Verification of Multi-Agent Distributed Systems”, Fundamenta Informaticae, 43:1-4 (2000), 195-214.
17. Nehaniv C. L., “Asynchronous Automata Networks Can Emulate Any Synchronous Automata Network”, Int. J. of Algebra and Computation, 14:5-6 (2004), 719-739.
18. Petri C. A., Kommunikation mit Automaten. PhD thesis, Bonn Institute f¨ur Instrumentelle Mathematik, 1962.
19. Valk R., “Petri Nets as Token Objects: An Introduction to Elementary Object Nets” (ICATPN’98), Lecture Notes In Computer Science, 1420 (1998), 1-25.
Review
For citations:
Bashkin V.A. On the Spatial Boundedness of Cellular RDA-nets. Modeling and Analysis of Information Systems. 2017;24(4):391-409. (In Russ.) https://doi.org/10.18255/1818-1015-2017-4-391-409
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