Peter Linz Edition 4 Exercise 3.1 Question 16.d (Page No. 76)

Question

Find a regular expression over Σ ={a,b,c} for all strings that contain no run of a's of length greater than 2. 

Here a run in a string is a sub string of length at least two as long as possible and consisting entirely of the same symbol. For eg, the string abbbaab contains a run of b's of length three and a tun of a's of length two.

Comments

that do not contain "aaa" .

Answer 1

(b+c+ab+ac+aab+aac)*(∊+a+aa)

Comments

The alphabet is {a,b,c}. So I guess extending your answer to (b+c+aab+aac+ab+ac)* (ϵ + a +aa ) will do. Right?

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yes missed 'c'.... now edited 

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thanks :)

Answer 2

Is this correct?

( (b+c) (b+c)* (aa +a) )*(λ+b+c)  +a+λ

Comments

Your regular expression isn’t clear. Also how will you generate the string $aab$ ?

Answer 3

$RegEx$ : $(∈ + a + aa) [(b+c)^+ a + (b+c)^+ aa ]^* (b+c)^*$