Automation of Algorithmic Tasks for Virtual Laboratories Based on Automata Theory

Abstract

In the work a description of an automata model of standard algorithm for constructing a correct solution of algorithmic tests is given. The described model allows a formal determination of the variant complexity of algorithmic test and serves as a basis for determining the complexity functions, including the collision concept – the situation of uncertainty, when a choice must be made upon fulfilling the task between the alternatives with various priorities. The influence of collisions on the automata model and its inner structure is described. The model and complexity functions are applied for virtual laboratories upon designing the algorithms of constructing variant with a predetermined complexity in real time and algorithms of the estimation procedures of students’ solution with respect to collisions. The results of the work are applied to the development of virtual laboratories, which are used in the practical part of massive online course on graph theory.