Finite Automata

Question

( a*+b*+a*b*+b*a* )    can we derive string abab and abba  from this regular expression. what is the relationship between  ( a*+b*+a*b*+b*a* ) and (a+b)*

Comments

no . ( a*+b*+a*b*+b*a* )    can not produce abab or abba.

And languages produced by ( a*+b*+a*b*+b*a* )   are subset of languages produced by (a+b)* .

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how did you analize can you tell a bit more(break it down into steps). I m having trouble understanding RE.

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How can I create a DFE for this RE .

Answer 1

( a*+b*+a*b*+b*a* ) cannot generate ((ab)⁺(ba)⁺)* or ((ba)⁺(ab)⁺)*  means here we can generate either string from (ab)* or (ba)* but cannot take both

But (a+b)* can generate all strings. So, we can define it as ∑*

Comments

How can I create a DFE for this RE .