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= { a , b }L = { w # a ( w ) = # b ( w ) } — w has the sam

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= { a , b }
L = { w * : # a ( w ) = # b ( w ) } w has the same
number of a\'s and b\'s.
L = { w * : # ab ( w ) = # ba ( w ) } w has the same
number of occurrences of ab and ba substrings.
1. Create a state diagram for the FSM that recognizes L ,
or prove n o such FSM is possible using the Pumping
Theorem.
2. Create a state diagram for the FSM that recognizes L ,
or prove no such FSM is possible using the Pumping
Theorem.
Solution
PUMPING THEOREM
For any regular language L there exists an integer n, such
that for all x belongs to L with |x| >= n, there exist u,v,w
such that
1) x=uvw
2) |uv|<= n
3)|v| >=1
4)for all i>=0, uviw belongs to L
given
1)
let x= aabb

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= { a , b } L = { w * : # a ( w ) = # b ( w ) } — w has the same number of a\'s and b\'s. L = { w * : # ab ( w ) = # ba ( w ) } — w has the same number of occurrences of ab and ba substrings. 1. Create a state diagram for the FSM that recognizes L , or prove n o such FSM is possible using the Pumping Theorem. 2. Create a state diagram for the FSM that recognizes L , or prove no such FSM is possible using the Pumping Theorem. Solution PUMPING THEOREM For any regular language L there exists an integer n, such that for all x belongs to L with |x| >= n, there exist u,v,w such that 1) x=uvw 2 ...
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