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For a context free grammar $G$ and two sentential forms $w_{1}$ and $w_{2}$ we define the relation $\Rightarrow<$ as follows: $w_{1} \Rightarrow

For a context free grammar $G$ and two sentential forms $w_{1}$ and $w_{2}$ we define the relation $\Rightarrow<$ as follows: $w_{1} \Rightarrow

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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For a context free grammar $G$ and two sentential forms $w_{1}$ and $w_{2}$ we define the relation $\Rightarrow<$ as follows: $w_{1} \Rightarrow<w_{2}$ if $w_{1}=X w$ for a variable $X$ an Sw \in(V \cup T)^{*}$, there is a production $X \rightarrow w^{\prime}$ in $GS, and $w_{2}=w^{\prime} w$. We also define the relation $\Rightarrow{ }_{<}^{*}$ so that $x \Rightarrow{ }_{<}^{*} y$ if there exists a sequence $w_{1}, w_{2}, \ldots w_{t}$ so that $x \Rightarrow{ }_{<} w_{1} \Rightarrow_{<}$ $w_{2} \Rightarrow<\cdots \Rightarrow<w_{t} \Rightarrow<y .$ Let $G$ be a context free grammar in CNF. Explain why for every $X \in V$ the language $\left\{w \in(V \cup T)^{*}: X \Rightarrow{ }_{<}^{*} w\right\}$ is regular. cs. vS.1188
Transcribed Image Text:For a context free grammar $G$ and two sentential forms $w_{1}$ and $w_{2}$ we define the relation $\Rightarrow<$ as follows: $w_{1} \Rightarrow<w_{2}$ if $w_{1}=X w$ for a variable $X$ an Sw \in(V \cup T)^{*}$, there is a production $X \rightarrow w^{\prime}$ in $GS, and $w_{2}=w^{\prime} w$. We also define the relation $\Rightarrow{ }_{<}^{*}$ so that $x \Rightarrow{ }_{<}^{*} y$ if there exists a sequence $w_{1}, w_{2}, \ldots w_{t}$ so that $x \Rightarrow{ }_{<} w_{1} \Rightarrow_{<}$ $w_{2} \Rightarrow<\cdots \Rightarrow<w_{t} \Rightarrow<y .$ Let $G$ be a context free grammar in CNF. Explain why for every $X \in V$ the language $\left\{w \in(V \cup T)^{*}: X \Rightarrow{ }_{<}^{*} w\right\}$ is regular. cs. vS.1188
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