Figure A.11
A.6 Moore Machine Minimization
The minimization of a Moore machine follows the pattern of the minimization of
Mealy machines, but there are some differences. While Definition A.5 and A.6
apply to Moore machines, Theorem A.4 needs to be modified.
Theorem A.6
(a) Two states q i and q j of a Moore machine are 0-distinguishable if
(b) the two states are k-distinguishable if they are (k – 1)-distinguishable or if
there exists an a ∈ ∑ such that δ(q i , a) = q r and δ(q j , a) = q s , where q r and q s are
(k – 1)-distinguishable.
Proof: The argument here is essentially the same as in Theorem A.4.
For the Moore machine minimization we first use the Mealy machine
A.6 Moore Machine Minimization
The minimization of a Moore machine follows the pattern of the minimization of
Mealy machines, but there are some differences. While Definition A.5 and A.6
apply to Moore machines, Theorem A.4 needs to be modified.
Theorem A.6
(a) Two states q i and q j of a Moore machine are 0-distinguishable if
(b) the two states are k-distinguishable if they are (k – 1)-distinguishable or if
there exists an a ∈ ∑ such that δ(q i , a) = q r and δ(q j , a) = q s , where q r and q s are
(k – 1)-distinguishable.
Proof: The argument here is essentially the same as in Theorem A.4.
For the Moore machine minimization we first use the Mealy machine