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Concept of Industry 4.0 includes the creation of cyber-physical systems, capable to decentralized control over production, sales, etc., as well as self-education and self-development. Such systems' functioning requires similar "smart" technologies for information storing and distributing. Due to decentralization support, ensuring cybersecurity for cryptocurrency and creating environment for "smart" contracts, blockchain was considered as a fast solution. But blockchain's projection from the narrow scope of digital money to general purpose technology for industry and public sector faced serious difficulties. Some of them can be overcome by partial improving within the present generation of blockchain (e.g. - amending consensus' algorithms). Others require significant transformations of the core technology, coupling it with other innovations in computer science and industry. Difficulties of transition phase gave rise to criticism and even led to rejections to use blockchain in practice. Then some hybrid solutions appeared, which took only a part of blockchain's innovative idea (blocks-organized ledger) and implanted it onto old-fashioned technologies (abandoning the idea of distributed architecture). It is offered to consider such solutions as an inferior "quasi-blockchain". The evolution of blockchain has been studied and it has been proven that the development of its decentralized versions is most compatible with concept of Industry 4.0. However, industrial application of such versions, as it is shown in the paper, is hampered by the internal contradictions: blockchain "trilemma" plus inefficient energy use. Prospects for getting out of "blockchain trilemma" impasse have been explored, including some modern innovative solutions, such as the Level-2 protocol (Lightning Network). The evolution scenarios for such innovations are described. A classification, which links blockchain to classical distributed databases and takes into account the logic of their development, is proposed. The most promising fields for blockchain industrial applications, including digital invoices (e-Invoice) and Industrial Internet of Things, are studied. The research, conducted in the paper, has helped to develop a criteria to select and optimize specific blockchain solutions for industrial applications. [ABSTRACT FROM AUTHOR]

The key features of the concept of Industry 4.0 development at the enterprises of machinebuilding industry were singled out. The analysis of mathematical models on classes of typical tasks for use at the construction of smart enterprises in the machine-building industry were carried out. It was determined, that in the process of ensuring the innovative development of machinebuilding enterprises within the Industry 4.0 framework it is necessary to use mathematical models, appropriate to machine vision technologies, robotic equipment, automated and intelligent production and control systems within the framework of enterprises’ cyberphysical systems. Such cyberphysical systems should be connected to the outside world through sensors and actuators, receiving data streams from the physical world, establishing and continuously updating the virtual twin of the physical world and including the possibility of interaction in reality according to instructions from the virtual sphere. This will allow ensuring the possibility of joint work, adaptation and development of all enterprise’s systems to improve working conditions, product quality, reduce labour requirements and increase the efficiency of manufacturing process of machine- building enterprises. The introduction of the above classes of mathematical models within the framework of cyberphysical systems must be carried out according to innovations in machinebuilding enterprises, which will ensure the automation of manual labour, the renewal of the already used innovative technologies and their unification in a single information space. The resulted models demand adaptation and the further development according to those innovative decisions, which will define a management of specific machine-building enterprises, depending on the specificity of the enterprise. Recommendations were given to the heads of machine-building enterprises on the use of mathematical models in the process of introducing the concept of smart-enterprises in the Ukrainian machine-building industry. Prospective directions of research were outlined in the paper. [ABSTRACT FROM AUTHOR]