Finite Automata and Regular Grammars

Abstract

In this chapter we introduce the notions of the deterministic finite automata and the nondeterministic finite automata, and we show their equivalence (see Theorem 2.1.14 on page 29). We also prove the equivalence between deterministic finite automata and S-extended type 3 grammars. We introduce the notion of a regular expression (see Section 2.5 on page 41) and we prove the equivalence between regular expressions and deterministic finite automata. We also study the problem of minimizing the number of states of the finite automata and we present a parser for type 3 languages. Finally, we introduce some generalizations of the finite automata and we consider various closure and decidability properties for type 3 languages.