Question

Prove/disprove for any regular expressions R and S: (a) (R + S)∗S = (R∗S)∗ (b) (R...

Prove/disprove for any regular expressions R and S: (a) (R + S)∗S = (R∗S)∗ (b) (R + S)∗ = (R∗S)∗

Note: when disproving a statement, you must give a concrete example of R and S, meaning a definition of R and S over some chosen alphabet.

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Answer #1

a) Incorrect

Counter Example

R = aa

S = bb

(R + S)∗S is not generating epsilon

(R∗S)∗ is generating epsilon

b) Incorrect

Counter Example

R = aa

S = bb

(R + S)* generates RR = aaaa

(R*S)* doesn't generate RRR

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