GATE CS 2024 Set 1 — Question 59
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Theory of Computation → Context-Free Languages → Chomsky Normal Form
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Question
Let be a context-free grammar in Chomsky Normal Form with and containing 10 variable symbols including the start symbol . The string is derivable from . The number of steps (application of rules) in the derivation is _________
Correct answer
179 to 179
Solution
In a Context-Free Grammar (CFG) in Chomsky Normal Form (CNF), every production is of the form
A → BC or , where and .To derive a string of length :1.We need applications of rules of the form
A → BC to generate a sentential form with variables. Starting from the start symbol (1 variable), each such rule application increases the number of variables by exactly 1. Thus, to reach variables, we need steps.2.We need applications of rules of the form to replace each of the variables with a terminal symbol from .
Total number of steps = .Given the string , its length .Number of steps = .Note: The total number of variables in (which is 10) is irrelevant to the number of steps in the derivation of a specific string.Continue learning with Success Tracker
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