Ontology View on Automata Theory

The summary of automata theory ontology is presented in the paper. It is based on the following dependences: a type of an automaton – the language accepted by the automaton – applications. The given ontology does not claim to be exhaustive as automata theory is very extensive and it is a complicated problem to survey all its aspects within one article. Only the main properties of automata and their applications are considered.

Minimization of Reactive Probabilistic Automata

The problem of finite automata minimization is important for software and hardware designing. Different types of automata are used for modeling systems or machines with finite number of states. The limitation of number of states gives savings in resources and time. In this article we show specific type of probabilistic automata: the reactive probabilistic finite automata with accepting states (in brief the reactive probabilistic automata), and definitions of languages accepted by it. We present definition of bisimulation relation for automata's states and define relation of indistinguishableness of automata states, on base of which we could effectuate automata minimization. Next we present detailed algorithm reactive probabilistic automata’s minimization with determination of its complexity and analyse example solved with help of this algorithm.