Finite Automata – Definition and Examples Lecture 6 Section 1.1 Mon, Sep 3, 2007

Definition of a Finite Automaton A finite automaton is a 5-tuple (Q, , , q 0, F), where Q is a finite set of states,  is a finite alphabet,  : Q    Q is the transition function, q 0 is the start state, and F  Q is the set of accept states.

Definition of a Finite Automaton Describe the automatic door formally. Describe the canal lock formally.

Regular Languages The language of a DFA is the set of all strings that it accepts. A regular language is a language that is recognized by some DFA.

Examples Design finite automata that will recognize the following languages over {a, b}. All strings that start with a. All strings that end with a. All strings that contain aaa. All strings in which each a is followed immediately by b.

Examples Over the alphabet of ASCII symbols. All strings that represent C++ identifiers. All strings that represent C++ ints. All strings that represent C++ floats.