Test by Bikram | Theory of Computation | Test 1 | Question: 19

Question

Consider the following CFG :
$S \rightarrow AB$
$A \rightarrow BC \mid a$
$B \rightarrow CC \mid b$
$C \rightarrow a \mid AB$

The Rank of Variable $A$ is:

• A. $2$
• B. $3$
• C. $4$
• D. not possible to define

Comments

Thanks...it is clear to me now!!

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@vijaycs here we are getting end of tree

in some transition....so that height we will not consider?

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Cycle present

Answer 1

if we make a precedence graph for this grammar, there is a loop between A and C, hence we can't conclude the rank of A.
Hence (D) is correct answer!

Comments

what exactly rank of a non terminal is??

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does rank of a non teminal  mean length of longest terminal string generated by it?

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if option have infinity also

then ans will be infinity??

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YES ,I  THINK SO!!