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Consider the CFG used in the proof of the pumping lemma. We want to choose a string long enough so that it is a string generated by the CFG and at least one variable repeats in a parse tree of the string. If no such string exist for this CFG, what can you say about the CFG?

Consider the CFG used in the proof of the pumping lemma. We want to choose a string long enough so that it is a string generated by the CFG and at least one variable repeats in a parse tree of the string. If no such string exist for this CFG, what can you say about the CFG?

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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Question 1 Consider the CFG used in the proof of the pumping lemma. We want to choose a string long enough so that it is a string generated by the CFG and at least one variable repeats in a parse tree of the string. If no such string exist for this CFG, what can you say about the CFG? O The CFG's language must be finite. There is no possibility of this happening: there always is such a string. O The CFG's language may or may not be infinite. O None of the above. O Then there is at most 1 variable that produces a single teminal in the CFG.
Transcribed Image Text:Question 1 Consider the CFG used in the proof of the pumping lemma. We want to choose a string long enough so that it is a string generated by the CFG and at least one variable repeats in a parse tree of the string. If no such string exist for this CFG, what can you say about the CFG? O The CFG's language must be finite. There is no possibility of this happening: there always is such a string. O The CFG's language may or may not be infinite. O None of the above. O Then there is at most 1 variable that produces a single teminal in the CFG.
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