An Intro. to formal lang. and automata(Peter Linz) chapter 2.....2.1 ques 6

Question

With Σ = {a,b}, give a dfa for L= w1aw2  :|w1|≥ 3,|w2|≤ 5

Answer 1

L = {W1aW2 | W1>=3 and W2<=5}

Comments

It doesnt say that w2 doesnt contain a's but with your dfa no language with w2 containing a's will get accepted.i think some modification is required

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after 'a' there should be atmost 5 b's..if 'a' is coming in W2 that will be merge to 'W1a'

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here they didn't say that you should not have 'a' 's in w2 so how can we merge it??

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You can try all strings belonging to L are getting accepted!!!!!!!

Answer 2

verify both valid string they are accepted and also verify that invalid string that is not getting accepted.

Answer 3

The  DFA  will be