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Finite Automata limitations


drwho

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I am trying to clear something that seems to be a little misleading for me.

 

I know the language over {a,b} consisting of all words containing the same number of occurrences of

the symbol a as of the symbol b is not regular.

 

I know that the language L over {a,b} consisting of all words containing

the same number of occurrences of ab as a substring as occurrences of ba as a substring

actually is regular.

 

What would be the best way to prove this? by finding a finite automaton that accepts this language?

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