From the Editor

Abstract

All the papers in this issue of the JIOS Journal may fit into the Science as Usual categoryand are therefore not going to be dealt with in detail in the introduction. However, for oneof the papers included an exception has been provided, namely the paper Sigma-notationand the equivalence of P and NP classes by Miron Ivanovich Telpiz. The circumstancesleading to its publication in this issue of JIOS are presented by the editors in this preface.It is generally acknowledged that, ever since it was defined by S. Cook over thirty yearsago, P = NP has presented one of the major open problems in computing science andinformation science in general. Whereas, on one hand, this problem presents a formidablechallenge to any scientist dealing with it, its solution, especially in case it should turn out tobe a positive one considering that current technology tends to evolve in a practicaldirection and its overall functioning is conducted implicitly under the assumption of anegative solution would have a major impact on the development of informationtechnology as well as the wider context of human society as a whole. Apart from being putforward in conferences, both positive and negative “solutions” to P = NP problem can beoccasionally found in press, scientific and professional journals. The web page titled “Pversus-NP Page” (see http://www.win.tue.nl/~gwoegi/P-versus-NP.htm) provides anexcellent source for this issue. It contains links to papers stating that P = NP, as well asthose contradicting the opposite, i.e., stating that P NP. Furthermore, references are givento Oded Goldreich's rationale behind his decision not to review papers proposing solutionsto P = NP problem and related difficult problems because, in his own words, they “alsoattract the attention of non-experts, and one annoying consequence is a flood of falseclaims of resolutions of these problems” (see http://www.wisdom.weizmann.ac.il/~oded/faq.html). Dr. Goldreich a recognised figure amongmathematicians of our time – recommends other scientists to follow his example when thisissue is concerned. Nevertheless, his arguments (at least those regarding non-experts) aredefinitely not to be acknowledged in the case of the work of the Russian mathematician andlogician Miron Ivanovich Telpiz, (see http://www.tarusa.ru/~mit/ENG/eng.php for details),who has been developing his positionality theory for functions, with a special emphasis onBoolean functions, for over two decades. While doing so, he has been drawing its(primarily conceptual) analogy to positionality theory for number systems. Building on hisextensive theory, which is combinatory very complex one indeed, Dr. Telpiz states theproof of P = NP. The underlying theory itself was proposed in the first volume of his bookPositionality principle for notation and calculation the functions, originally published inRussian by the Institute of Space Researches of the Russian Academy of Science. It was dueto this book that contacts between a member of the Editorial Board and Dr. Telpiz, as wellas Dr. Andrej Fomin, his assistant and associate, were established. During those contactsthe idea evolved of Dr. Tepiz delivering an invited lecture at the IIS2004 Conference.Annual IIS Conferences have been organized by the Faculty of Organization andInformatics for years. A lecture on proving the statement P = NP was arranged.Unfortunately, Dr. Telpiz was eventually not capable of giving the lecture. Nevertheless, heproposed for his lecture to be published in form of an article in the JIOS Journal. Uponreceiving the Russian version of his article named Sigma-notation and the equivalence of Pand NP classes, the Editorial Board had it translated into English and proceeded to havingit reviewed. The paper was sent to several renowned world experts in the field of Booleanfunctions, mathematical logic and algorithm theory for review. Yet, no response wasreceived from reviewers contacted although the Editorial Board and Dr. Telpiz made effortsfor access to all relevant papers, as well as the book itself, to be possible. Bearing in mindnot only the great relevance of P = NP problem but also the constant need for scientificideas and findings to be disseminated, the JIOS Editorial Board has decided to have Dr.Telpiz's paper published although it had not been officially reviewed, which the authorhimself has consented to in writing. Owing to its inclusion in this issue, the paper is beingpresented to a wider scientific and professional audience who are thus given an opportunityto both consider and assess it from their own perspective.Editors