The idea of continuation of positionality principle has arisen for a long time: in first half of 1978. The first software on recognition of feasibility were created in middle of 1987 by I.V.Petrov on the algorithms using idea of positionality. The researches which are carried out at that time are reflected in part in Pr-1612 by Institute space researches Academy of Science the USSR: O.M.Moskalenko, I.V.Petrov, M.I.Telpiz, V.I.Shevchenko: Development on the basis of positional algebra of logic of algorithms of a problem for satisfiability and their statistical research. - 1990. - 36 pages.
Mostly theoretical research, but in partial reflected in software the research directed on definition of perspective possible ways of development of idea of positionality, began to develop in harmonous enough theory by 1995, when the material, which has made a basis of the book [PP], began to collect. Then the basic objective of the book, consisting in system engineering of notation and calculation of functions basing an positional principle, was formulated.
At first functions of algebra of logic were chosen and for their representation such system production (forming rules) is developed which allows simply enough (with linear complexity) to write down classical formulas of propositional logic through the positional operators, constructed from production. For performance of transformations above positional operators the system of coproductions (this name is accepted for a composition of production) and system of combinators (combinations of production) is entered.
Coproductions and combinators are expansion of system productions and simply enough allow to carry out transformations above positional operators.
Especially big attention is given to the transformations in particular equivalent to transformations (equivalent we name transformations above formulas of propositional logic which do not change the tables of true of these formulas).
Development of the expanded system of productions, allowing not only to write down operators, but also effectively to carry out equivalent transformations above them, makes one of directions of development positionality. Another is connected to development of such positional notation which can be considered as limiting expansion or as full positionality for representation of logic functions. These both directions form complete system which makes the basic contents of the book and is that required discovery about which there is a speech in the citation given in item 2 from [15].
As the basis for this statement the constructive proof of can serve contained in the book [PP] that NP-complete problems are solved on polynomial algorithm. Such constructive algorithm is given for problem of SAT (satisfiability). As is known (see [13] or [15]) under theorem Cook SAT-problem is NP-comlete problem. Even about a theorem NP=P see item. 4.
The book [PP] contains also even more interesting algorithm. It with polynomial time complexity carries out superreduction SAT-problem (superreduction of a problem is its such equivalent transformation as a result of which the text of a task degenerates if it is inconsistent, or becomes such that carrying out set is under construction with linear time complexity).
When we speak about SAT-problem that it superrected, it is necessary to understand as it that a problem became extralight.
Even about a superreduction see item 5.
The estimation of this consequences of results and what can appear on base of already developed theory to the full now is hardly possible. Only it is possible to tell that for realization of many grandiose projects the main obstacle is removed. For example, the Japanese project is sold to the full and even more courageous projects which can be expected are sold.
One is indisputable. The subjects of scientific researches in computer science should change sharply. The concept underlying designing both element base of computers and computers should change.
The concept of programming languages should change meaning that such languages become languages of computers and will be moving off from the person. They in the structure, I hope, will include as one of the important elements positional language of the operators which stated in the book.
And, at last, the most important. This book containing positional language of notation and calculation of operators and allowing to solve the mentioned above problems is not last word in development positionality, but faster it only began. And that it was valid the beginning necessary to acquire and distribute the received results and the book should this promote.
The book is in a stage of end (such end should be held already more than half-year back), but as some ideas and results remain it not covered and the volume grows, their statement solved to transfer to the second volume.