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Infinite Petri Nets
October 11, 2017 @ 11:00 am - 12:01 pm
Infinite Petri Nets
Visiting Professor, Fulbright Schiolar
University of Tennessee, Knoxville
A composition and analysis technique was developed for investigation of infinite Petri nets with regular structure, introduced for modeling networks, clusters and computing grids, that also concerns cellular automata and biological systems. A case study of a square grid structure composition and analysis is presented. Parametric description of Petri nets, parametric representation of infinite systems for the calculation of place/transition invariants, and solving them in parametric form allowed the invariance proof for infinite Petri net models. Some additional analysis techniques based on graphs of transmissions and blockings are presented. Further generalization on multidimensional structures such as hypercube and hypertorus implemented. Generators of Petri net models developed and put on GitHub for public use. Complex deadlocks were disclosed and a possibility of network blocking via ill-intentioned traffic revealed. Prospects for further development of infinite Petri net theory are outlined.
Dmitry A. Zaitsev received the Eng. degree in applied mathematics from Donetsk Polytechnic Institute, Donetsk, Ukraine, in 1986, the Ph.D. degree in automated control from the Kiev Institute of Cybernetics, Kiev, Ukraine, in 1991, and the Dr.Sc. degree in telecommunications from the Odessa National Academy of Telecommunications, Odessa, Ukraine, in 2006. Since 2009, he has been with International Humanitarian University, Odessa, Ukraine, where he is currently a Professor of Computer Engineering. Since 2009, he has been with Vistula University, Warsaw, Poland, where he is currently a Professor of Computer Science. He developed generalized neighborhood for cellular automata, universal Petri nets, the analysis of infinite Petri nets with regular structure, the decomposition of Petri nets in clans, and the method of synthesis of fuzzy logic function given by tables. His current research interests include Petri net theory and its application in networking, production control, and computing. He is a senior member of ACM. His CV, publications, software, and models are put on his personal web-site http://daze.ho.ua
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