Abstract
Petri nets have been known for years as a model of concurrent systems but their computationally universal extensions are exponentially slow comparing Turing machines, especially when implementing arithmetic operations. A Sleptsov net concept, suggested quarter a century ago, recently acquired its second birth due to its ability of fast implementation of basic arithmetic operations. Firing a transition in a few instances at a step leads to universal constructs which run in polynomial time. In Sleptsov net computing, a program, written in Sleptsov net language preserving concurrency of an application area, runs on Sleptsov net processor which implements concurrent firing of transitions in multiple instances providing fast computations. Motivation for new models of hyper-computations is presented. Sleptsov net is introduced compared to Petri and Salwicki nets.
A concept of universal Sleptsov net, as a prototype of a processor in Sleptsov net computing, is discussed. A small universal Sleptsov net that runs in polynomial time is constructed; it consists of 13 places and 26 transitions. Principles of programming in Sleptsov nets, as composition of reverse control flow and data, are developed. Standard control flow patterns include sequence, branching, loop, and parallel execution. Basic modules, which implement efficiently copying, logic, and arithmetic operations, are developed. Special dashed arcs are introduced for brief specification of input and output data of modules (subnets). Ways of hierarchical composition of a program via substitution of a transition by a module are discussed. Examples of Sleptsov net programs for data encryption, fuzzy logic, and partial differential equations are presented. Enterprise implementation of Sleptsov net computing promises ultra-performance. (History of Sleptsov nets)
https://www.igi-global.com/newsroom/archive/highest-standard-sleptsov-software/3199/
Basic publications
Zaitsev D.A. Sleptsov Net Computing (pp. 7731-7743) Chapter 672 in Mehdi Khosrow-Pour (Ed.)
Encyclopedia of Information Science and Technology, Fourth Edition (10 Volumes). IGI-Global:
USA, 2017.
Zaitsev D.A. Sleptsov Nets Run Fast, IEEE Transactions on Systems, Man, and Cybernetics:
Systems, 2016, Vol. 46, No. 5, 682 – 693.
Bio
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 2014, 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
