On the Size of Deterministic Finite Automata

The number of states of a deterministic finite automaton, which is equivalent to a nondeterministic finite automaton is bounded by 2n, where n is the number of states of the nondeterministic finite automaton. This bound is very pesimistic. Some subclasses of finite automata are shown, for which the complexity of determinization is far lower. On the base of pioneering idea of homogenous finite automata, two classes of finite automata are defined and the complexity of their determinization are shown. These classes are called generalized homogenous finite automata and semihomogenous finite automata.