Let G = (V, T, S, P) be a context-free grammar such that eve...

MCQ

Let G = (V, T, S, P) be a context-free grammar such that every one of its productions is of the form A ? ?, with |?| = k > 1. The derivation tree for any string W ? L (G) has a height such that

h<((|W| - 1)/k-1)

log_k|W| < h

log_k|W| < h < ((|W| - 1)/k-1)

log_k|W| <= h <= ((|W| - 1)/k-1)

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MCQ

Consider the following grammars G1 and G2 respectively. Grammar - G1:

A1 ? A2A3
A2 ? A3A1 | b
A3 ? A1A1 | a

Grammar - G2:

S ? AA | 0
A ? SS | 1

Consider the following statements regarding above grammars: (I): This grammar is not left recursive and equivalent to grammar - G1:

A1 ? A2A3
A2 ?  A3A1 | b
A3 ? a | bA3A1 | aK | bA3A1K 
k ? A1A3A1 | A1A3A1K

(II): This grammar is not left recursive and equivalent to grammar - G2:

S ? A A | 0
A ? 0S | 1 | 0SK | 1K
K ? AS | ASK

Only statement (I) is correct

Only statement (II) is correct

Both statements (I) and (II) are correct

Neither statement (I) not (II) is correct

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Consider the following context-free grammar over the alphabet ? = {a, b} with S as the start symbol:

S ? AT 
A ? aAa | bAb | #T 
T ? aT | bT | ?

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{ w#x | w is a substring of x, where w, x ? {a, b}* }

x#w | w^R is a substring of x, where w, x ? {a, b}* }

{ w#x | w, x ? {a, b}* }

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