Anbar University/College of Computer 2012-2013 Computational Theory Lecture note
Lecture eight Lecturer: Dr Ali Jbaeer Dawood
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Theory of Computational
Finite Automata with Output
Lecture Objective
Moore Machines
Mealy Machines
Moore = Mealy
Moore Machine Definition:
Moore machine is a collection of five things:
1. A finite set of states q0, q1, q2, ..., where q0 is designated as the start state.
2. An alphabet of letters for forming the input string = {a, b, c, …}.
3. An alphabet of possible output characters Γ = {0, 1, 2, …}.
4. A transition table that shows for each state and each input letter what state is
reached next.
5. An output table that shows what character from Γ is printed by each state as it is
entered.
Notes:
• We did not assume that the input alphabet is the same as the output alphabet Γ.
• To keep the output alphabet separate from the input alphabet, we give it a
different name Γ (instead of ∑) and use number symbols {0, 1, …} (instead of
{a, b, …}).
• We refer to input symbols as letters, whereas we refer to output symbols as
characters.
• We adopt the policy that a Moore machine always begins by printing the
character dictated by the mandatory start state. So, if the input string has 7 letters,
then the output string will have 8 characters, because it includes 8 states in its
path.
• A Moore machine does not define a language of accepted words, because there is
no such thing as a final state.
• Every possible input string creates an output string. The processing is terminated
when the last input letter is read and the last output character is printed.
• There are some subtle ways to turn Moore machines into language definers.
