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Dr. Dmitry Zaitsev sacrifices his ego to expose computer science achievements in Ukraine

Selfie with a view on “Cybernetics and Systems Analysis”

By IGI Global on Sep 27, 2016

Contributed by Dmitry Zaitsev (International Humanitarian University, Ukraine), Editor of the video lecture series Petri Nets for Modeling and Computing, author of "Infinite Petri Nets as Models of Grids" and "Composition of Functional Petri Nets".

Selfies are all the rage recently, though many people resent seeing suchlike narcissistic affairs. The topic of most selfies is “me and something remarkable”, but many of them even suffer from ignoring any background with the only topic being: “I am surprisingly beautiful with this peculiar grimace”.

But when witnessing and being a part of something that requires major public attention, sometimes a measure of ego is necessary. I am attempting to avoid such excessive selfishness in my "selfie" and pay due respect to my contemporary - the best CS journal in Ukraine, which has been published since 1965. Cybernetics and Systems Analysis (CSA) is the only CS Ukrainian journal indexed in Scopus and included in JCR 1997-1999. I like to believe that this is because during those years we published a couple of papers [1,2] in it. In spite of the fact that the journal is republished and translated in English by Springer, it lays aside the citation thoroughfares of the civilized world. Sometimes good results published in CSA remain unheeded for years because very few scientists look inside it.

Ukraine has solid background in Computer Science, established with the first in the continental Europe computer MESM put into operation in 1951 in Kiev Laboratory of Sergey Lebedev. The further maintenance and development of the computer since 1956 was continued by Victor Glushkov, who headed Cybernetics Institute of National Academy of Science of Ukraine, created in 1962. The Institute, which established numerous branches in universities all around Ukraine, has become the center of Computer Science in Ukraine. It is widely known for its scientific achievements and bright scientists such as Zinoviy Rabinovich, Vladimir Skurihin, Igor Velbitsky, Ivan Sergiyenko, and others. It has developed new kinds of computer hardware and software and fulfilled numerous application projects for production control, management, and artificial intelligence. Interested parties can trace the implementation of “paperless management technology” and “state control system” as original concepts of Vladimir Glushkov. In 1965, a journal named Cybernetics was founded and renamed in Cybernetics and Systems Analysis in 1991.

We published our best results in CSA [1-7], considering it was the only journal in the world we could publish in before we learned English; otherwise we could not share our ideas easily to others. Originally the CSA papers were submitted and published in Russian with strict proofreading procedures often accomplished only with personal discussions on terminology, style, and phrasing. Then the papers were translated and published in English by Springer. An extensive process! Ergo, the proper time to take a selfie has come. Let us take a look at the papers I have published in CSA, together with my respected co-authors, during some twenty years.

Article [1] introduces a concept of a multichannel transition for Petri nets. Now I rather say the multiple firing strategy using an analogy with the maximal firing strategy of Salwicky. Recently, widespread papers on “the exhaustive use of rule” in spiking P neuron systems do not even mention our multichannel transitions which first appeared in my Ph.D., defended in 1991. We illustrate the concept for a timed Petri net where time delays are associated with transitions. We applied them for production control in our Opera-Topaz system from where they come quite naturally. Say we have a job to do for a duration of 10 minutes, modeled by a transition; we have 3 work-pieces and 4 machine tools. Why should we do it sequentially in 30 minutes, like in usual nets, when we can start processing 3 work-pieces on 3 machine tools simultaneously and finish the lot in 10 minutes? It looks like having unlimited number of each transition attached in parallel; moreover, usual Petri net is obtained as a special case via attaching a place having unit marking to each transition via a loop. We specified a state of such net using its marking and history of transitions’ firing that allowed us to compose a strict state equation to describe its behavior. Article [3] actually accomplishes results of article [1] with fundamental equation and invariants of timed nets with multichannel transitions. Similar to linear invariants of Petri nets, we introduced invariants of state and behavior, so-called full invariants, and considered partial invariants which preserve the marking only. Finally, properties of invariant nets have been investigated.

In addition, article [1] introduces a concept of functional equivalence for Petri nets, specifies the net transfer function, and presents an algebra that combines arithmetic, logic, and timed operations. Algebraic transformations of formulae correspond to structural transformations of a net preserving its transfer function, offering a new kind of reduction technique. The concept of functional equivalence introduced for definite subsets of input and output places a supplement's known kinds of equivalences considered for reachability trees and free languages of a net. Two articles [4] and [5] develop the topic of functional Petri net under a device “divide and sway”, respectively; namely [4] describes how to “divide” while [5] teaches how to “sway” afterwards. Among different types of subnets with contact places the functional subnet is the strictest one: input places have only output arcs and output places have only input arcs. We illustrated decomposition on models of networking protocols such as BGP and TCP. It was proven that a set of minimal functional subnets constitutes a basis and any functional subnet is obtained as a sum of some minimal subnets. For decomposition, two techniques have been offered: with logical equation and via ad-hoc algorithm of polynomial complexity. The advantage of the logical equations technique is its applicability for more general kinds of subnets with contact places. Because of strict limitation on the connection of a functional subnet, to analyze the properties of a net [5], we decompose it into a set of minimal functional subnets, analyze properties of each subnet, and, finally, solve a sole composition system in which dimension is equal to the number of contact places. The basic motivation is a speed-up of computations for big models.

In the state equation of a timed Petri net with multichannel transitions [1], we applied operations of continuous logic, namely, conjunction represented as the minimum operation. In this way we came to the task of synthesis of a continuous (fuzzy) logic function given in tabular form [2]. Synthesis of a binary logic function on its truth table is a well-known task. A continuous logic function can be given with a choice table where all the variants of reordering arguments and their negations with the great-or-equal operation are listed; on each variant a function takes the value of an argument or a negation of an argument. We introduced concepts of constituents of minimum and maximum, similar to classical constituents of zero and unit in binary logic, to compose PDNF and PCNF. To handle an essential difference that not any choice table gives a continuous logic functions, a necessary and sufficient condition was formulated in the terms of overlapping rows of the choice table. Finally, for any choice table we obtained a set of continuous logic functions valid on definite subareas.

In 2007-2008, we began working on a project supported by NATO in verification of complex networking protocols. We came to recognize the necessity of obtaining results, not only for a definite net, but for a definite structure. In article [6] we introduced a composition of Petri net models having hypercube structure with parameters specifying the number of dimensions and size. As far as we studied properties of solutions obtained for any natural values of parameters, we claimed working with infinite Petri nets. We studied grid structures composed of a model of generalized packet switching devices and built infinite systems of linear algebraic equations solved in nonnegative integer numbers. Parametric solutions have been obtained to study properties of infinite Petri nets; complex deadlocks caused by loops of blockings, chains of blockings, and isolation revealed.

Finally we came to programming in the language of Petri nets. For years a concept of a universal Petri net had been hanging in the air, its existence proven for the class of inhibitor nets. Article [7] presents a universal inhibitor Petri net specified in an explicit form. It is a prototype of a Petri net processor which is specified by a Petri net and executes a program written in the Petri net language. The language is appropriate for concurrent programming and model-driven approaches for software design. Lately, smaller universal nets consisting of a few dozen nodes were composed. However the advantage of a net described in [7] is the direct encoding of a program without references to other models of computation.

Perhaps it’s all done with the selfie. The camera zooms out to catch outstanding scientists in Ukraine who dislike selfies though “photographers” do not pay due attention to them. As Ukraine integrates into European and world structures and this process involves revolutionary scientific developments, scientists of Ukraine rely on the world’s welcome. Please view our journals, at least, translated and published in English, such as CSA, and cite our papers when it is appropriate.

References
1. Zaitsev D.A., Sleptsov A.I. State equations and equivalent transformations for timed Petri nets, Cybernetics and Systems Analysis, Volume 33, Number 5 (1997), 659-672, DOI: 10.1007/BF02667189
2. Zaitsev D.A., Sarbei V.G., Sleptsov A.I., Synthesis of continuous-valued logic functions defined in tabular form, Cybernetics and Systems Analysis, Volume 34, Number 2 (1998), 190-195, DOI: 10.1007/BF02742068
3. Zaitsev D.A. Invariants of Timed Petri Nets, Cybernetics and Systems Analysis, Volume 40, Number 2 (2004), 226-237, DOI: 10.1023/B:CASA.0000034448.97077.dd
4. Zaitsev D.A. Decomposition of Petri Nets, Cybernetics and Systems Analysis, Volume 40, Number 5 (2004), 739-746, DOI: 10.1007/s10559-005-0012-0
5. Zaitsev D.A. Compositional analysis of Petri nets, Cybernetics and Systems Analysis, Volume 42, Number 1 (2006), 126-136, DOI: 10.1007/s10559-006-0044-0
6. Zaitsev D.A., Shmeleva T.R. Verification of hypercube communication structures via parametric Petri nets, Cybernetics and Systems Analysis, Volume 46, Number 1 (2010), 105-114, DOI: 10.1007/s10559-010-9189-y
7. Zaitsev D.A. Universal Petri net, Cybernetics and Systems Analysis, Volume 48, Number 4 (2012), 498-511. DOI: 10.1007/s10559-012-9429-4

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Congratulation for all the hard work and all your achievements!

Toderici Melania6 years ago

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