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## Equivalence Checking Problem for Finite State Transducers

Finite state transducers over semigroups can be regarded as a formal model of sequential reactive programs. In this paper we introduce a uniform tech- nique for checking eectively functionality, k-valuedness, equivalence and inclusion for this model of computation in the case when a semigroup these transducers op- erate over is embeddable in a decidable group.

The author argues on expediency and mutual conditionality of evolutionary changes in the nature and in society. In the article three major factors of the evolution are allocated, namely: the accident, the factor of coincidence of circumstances and the factor of acceleration of social evolution.

The conference *Philosophy, Mathematics, Linguistics: Aspects of Interaction 2014 (PhML-2014)* is a sequel in the series of conferences intended to provide a forum for philosophers, mathematicians, linguists, logicians, and computer scientists who share an interest in cross-disciplinary research. The conference PhML-2014 is endorsed by the American National Committee of the Division of Logic, Methodology and Philosophy of Science (DLMPS) of the International Union of the History and Philosophy of Science (IUHPS), the Japan Association for Philosophy of Science, the Swedish National Committee for Logic, Methodology and Philosophy of Science.

The monograph is devoted to the consideration of complex systems from the position of the end the 21st century. The considerable breakthrough in the understanding of complex systems is comprehensively analyzed. Such a breakthrough is connected with the use of the newest methods of nonlinear dynamics, of organization of the modern computational experiments. The book is meant for specialists in different fields of natural sciences and the humanities as well as for all readers who are interested in the recent advancements in science.

A model for organizing cargo transportation between two node stations connected by a railway line which contains a certain number of intermediate stations is considered. The movement of cargo is in one direction. Such a situation may occur, for example, if one of the node stations is located in a region which produce raw material for manufacturing industry located in another region, and there is another node station. The organization of freight traﬃc is performed by means of a number of technologies. These technologies determine the rules for taking on cargo at the initial node station, the rules of interaction between neighboring stations, as well as the rule of distribution of cargo to the ﬁnal node stations. The process of cargo transportation is followed by the set rule of control. For such a model, one must determine possible modes of cargo transportation and describe their properties. This model is described by a ﬁnite-dimensional system of diﬀerential equations with nonlocal linear restrictions. The class of the solution satisfying nonlocal linear restrictions is extremely narrow. It results in the need for the “correct” extension of solutions of a system of diﬀerential equations to a class of quasi-solutions having the distinctive feature of gaps in a countable number of points. It was possible numerically using the Runge–Kutta method of the fourth order to build these quasi-solutions and determine their rate of growth. Let us note that in the technical plan the main complexity consisted in obtaining quasi-solutions satisfying the nonlocal linear restrictions. Furthermore, we investigated the dependence of quasi-solutions and, in particular, sizes of gaps (jumps) of solutions on a number of parameters of the model characterizing a rule of control, technologies for transportation of cargo and intensity of giving of cargo on a node station.

Event logs collected by modern information and technical systems usually contain enough data for automated process models discovery. A variety of algorithms was developed for process models discovery, conformance checking, log to model alignment, comparison of process models, etc., nevertheless a quick analysis of ad-hoc selected parts of a journal still have not get a full-fledged implementation. This paper describes an ROLAP-based method of multidimensional event logs storage for process mining. The result of the analysis of the journal is visualized as directed graph representing the union of all possible event sequences, ranked by their occurrence probability. Our implementation allows the analyst to discover process models for sublogs defined by ad-hoc selection of criteria and value of occurrence probability

The geographic information system (GIS) is based on the first and only Russian Imperial Census of 1897 and the First All-Union Census of the Soviet Union of 1926. The GIS features vector data (shapefiles) of allprovinces of the two states. For the 1897 census, there is information about linguistic, religious, and social estate groups. The part based on the 1926 census features nationality. Both shapefiles include information on gender, rural and urban population. The GIS allows for producing any necessary maps for individual studies of the period which require the administrative boundaries and demographic information.

Existing approaches suggest that IT strategy should be a reflection of business strategy. However, actually organisations do not often follow business strategy even if it is formally declared. In these conditions, IT strategy can be viewed not as a plan, but as an organisational shared view on the role of information systems. This approach generally reflects only a top-down perspective of IT strategy. So, it can be supplemented by a strategic behaviour pattern (i.e., more or less standard response to a changes that is formed as result of previous experience) to implement bottom-up approach. Two components that can help to establish effective reaction regarding new initiatives in IT are proposed here: model of IT-related decision making, and efficiency measurement metric to estimate maturity of business processes and appropriate IT. Usage of proposed tools is demonstrated in practical cases.