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Consider the regular expression $R = (a + b)^* (aa + bb) (a + b)^*$

Which deterministic finite automaton accepts the language represented by the regular expression $R$?

1. 2. 3. 4. edited | 2.4k views

DFA given in option A

Here, $S_3$ and $S_4$ are equivalent states and can be minimized.

This results in DFA given in:

https://gateoverflow.in/3523/gate2007-it_71

edited
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C. Is false since abb not accepted

D. Is false since as or bb not accepted

B.is false since it is not DFA

A. Is the ans .. S3 and S4 are similar States..minimum no.of states are 4
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right
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Option C will also not accept baa, abb etc.

A)  as it accepts anything (aa or bb )anything
So aa ,bb, aaa,aaaa bbb,bbbb,bbbbbb,bbaaaababba
ababababaababababa or abababababbb will be accepted
and only A satisfies.
Correct if Wrong,

lets try by elimination:

(B.) it accepts ab which is not in language

(C.) it is not accepting abb which is in language

(D.) it is not accepting aa which is in language

coming to option (A.) it accepts anything containing aa/bb

(B.) it accepts ab which is not in the language

(C.) it is not accepting abb which is in language and also  Is false since  baa, abb not accepted

(D.) it is not accepting aa and bb which is in language

coming to option (A.) it accept

Here,

Option B: it generates a string like ab which is not a part of our language, hence rejected.

Option C and D: they don't even accept the minimal length strings aa and bb of our language, hence rejected.

Option A is thus the right answer!