Consider the following context free grammar over the alphabet a b c with S as the start symbol S abScT abcT T bT b gate computer science 2017

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Consider the following context-free grammar over the alphabet ∑ = {a, b, c} with S as the start symbol: S → abScT | abcT T → bT | b -gate computer science 2017

Which of the following represents the language generated by the above grammar ?
A) {(ab)n(cb)n | n >= 1 }
B) {(abncbm1cbm2...cbmn | n, m1, m2, ....., mn >= 1 }
C) {(ab)n(cbm)n | n >= 1 }
D) {(ab)n(cbn)m | m, n >= 1 }


By:satyashiromani

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Answers

B) {(abncbm1cbm2...cbmn | n, m1, m2, ....., mn >= 1 }

Explanation: 
Let’s generate a string from given grammar : S → abScT → ab abScT cT → abab abcT cTcT → abababc bT cTcT → abababcb bT cTcT → abababcbb bT cTcT → abababcbbbb cTcT → abababcbbbbc b cT → abababcbbbbcbc bT → abababcbbbbcbcbb This string can rule out all wrong options. Now let’s try to analyse this string. → abababcbbbbcbcbb → {(abncbm1cbm2...cbmn | n, m1, m2, ....., mn >= 1 } We can clearly rule out option (A), (C) and (D) with help of the string generated by given grammar. Only option (B) is correct.


deepuckraj

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