Anatoly V. Anisimov

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The purpose of this paper is to consider a special kind of sorting problem in which a sequencea 1 ...a n is to be rearranged into an optimal order by interchanging pairs of adjacent elements, where certain pairs of elements are not allowed to commute with each other. Section 1 presents an informal example intended to clarify the nature of the problem, while(More)
With any finitely generated group presentation, one can associate a formal language (called the reduced word problem) consisting of those words on the generators and their inverses which are equal to the identity but which have no proper prefix equal to the identity. We show that the reduced word problem is a simple language if and only if each vertex of(More)
Formalizing mathematical argument is a fascinating activity in itself and (we hope!) also bears important practical applications. While traditional proof theory investigates deducibility of an individual statement from a collection of premises, a mathematical proof, with its structure and continuity, can hardly be presented as a single sequent or a set of(More)
Dealing with a formal mathematical text (which we regard as a structured collection of hypotheses and conclusions), we often want to perform various analysis and transformation tasks on the initial formulas, without preliminary normalization. One particular example is checking for “ontological correctness”, namely, that every occurrence of a nonlogical(More)
In this paper, the approach to the development of deductive assistance based on the current state of the System for Automated Deduction, SAD, is described briefly. The SAD may be considered as a three-dimensional "shell" for deductive assistance in a formal natural language environment when solving a number of scientific and industrial tasks requiring(More)
We offer novel algorithms for efficient encoding/decoding of variable-to-fixed length codes, requiring at most quadratic amount of space: O(L), where L is the depth of a coding tree. This is a major improvement compared to exponential O(2) usage of space by conventional techniques using complete representations of coding trees in computer’s memory. These(More)