Using interactivity in computer-facilitated learning for efficient comprehension of mathematical abstractions

Mathematical concepts often form a basis for creating more complex concepts. We address the problem of learning automata theory which is the starting point for understanding a number of natural and technical sciences. Mathematical abstractions used for defining and describing entities of automata theory and their interaction can present an uncrossable obstacle in the process of learning this basic knowledge. We have created a new teaching tool, "Automata Simulator", which is meant to help students in faster and better comprehension of the basics of automata theory that pose the greatest problem in understanding state machines in general. The student is given the freedom to design an arbitrary state machine by using an intuitive graphical user interface (GUI) and operate it by interactively controlling the tool. We present the tool and describe the implementation of the tool as a standalone application and as a client-server application in the global network environment (Internet).