Finite Automata Definition and Examples

1
Finite Automata Definition and Examples

• Lecture 6
• Section 1.1
• Mon, Sep 3, 2007

2
Definition of a Finite Automaton

• A finite automaton is a 5-tuple (Q, ?, ?, q0, F),
  where
• Q is a finite set of states,
• ? is a finite alphabet,
• ? Q ? ? ? Q is the transition function,
• q0 is the start state, and
• F ? Q is the set of accept states.

3
Definition of a Finite Automaton

• Describe the automatic door formally.
• Describe the canal lock formally.

4
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.

5
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.

6
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.