Algebraic School of V.M. Glushkov and Insertion Modeling

The Algebraic School of Viktor Mykhailovych Glushkov already has several generations of scientists, most of whom have already identified and are developing their own scientific directions. This school, started at the Institute of Cybernetics, was shaped by research that had the significance of inventions at the level of world science and the computer industry and in many ways predicted their further development. The work considers the formation of the paradigm of insertion modeling as a generalization of the main achievements of the Glushkov school, starting from the theory of automata and up to modern computer algebra systems. The main concepts from which insertion modeling was formed are considered, namely, symbolic computations, which were implemented even in the first personal machine of the MIR series. It is also the theory of agents and environments, parallel computing, and methods of artificial intelligence, developed at the Institute of Cybernetics, in the 60s and 70s. Numerous deployments of insertion modeling methods in cyber security, research in natural sciences, blockchain technology, in verification and testing of software and hardware, have shown the practicality and value of theoretical research conducted by followers of the Glushkov school. Keywords: symbolic computation, algebraic modeling, insertional modeling.