GATE | GATE CS 2018 | Question 65

A lexical analyzer uses the following patterns to recognize three tokens T₁, T₂, and T₃ over the alphabet {a,b,c}.

T₁: a?(b∣c)*a
T₂: b?(a∣c)*b
T₃: c?(b∣a)*c

Note that ‘x?’ means 0 or 1 occurrence of the symbol x. Note also that the analyzer outputs the token that matches the longest possible prefix.

If the string bbaacabc is processes by the analyzer, which one of the following is the sequence of tokens it outputs?

(A) T₁T₂T₃
(B) T₁T₁T₃
(C) T₂T₁T₃
(D) T₃T₃


Answer: (D)

Explanation: 0 or 1 occurrence of the symbol x.

T1 : (b+c)* a + a(b+c)* a
T2 : (a+c)* b + b(a+c)* b
T3 : (b+a)* c + c(b+a)* c

Given String : bbaacabc
Longest matching prefix is ” bbaac ” (Which can be generated by T3)
The remaining part (after Prefix) “abc” (Can be generated by T3)

So, the answer is T₃T₃

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