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191
Ullman (TOC) Edition 3 Exercise 7.4 Question 5 (Page No. 308)
Modify the $CYK$ algorithm to report the number of distinct parse trees for the given input, rather than just reporting membership in the language$.$
Modify the $CYK$ algorithm to report the number of distinct parse trees for the given input, rather than just reporting membership in the language$.$
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192
Ullman (TOC) Edition 3 Exercise 7.4 Question 4 (Page No. 308)
Show that in any $CNF$ grammar all parse trees for strings of length $n$ have $2n-1$ interior nodes $(i.e.,$ $2n-1$ nodes with variables for lables$).$
Show that in any $CNF$ grammar all parse trees for strings of length $n$ have $2n-1$ interior nodes $(i.e.,$ $2n-1$ nodes with variables for lables$).$
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193
Ullman (TOC) Edition 3 Exercise 7.4 Question 3 (Page No. 308)
Using the grammar $G$ of Example $7.34,$use the $CYK$ algorithm to determine whether each of the following strings is in $L(G):$ $ababa$ $baaab$ $aabab$
Using the grammar $G$ of Example $7.34,$use the $CYK$ algorithm to determine whether each of the following strings is in $L(G):$$ababa$$baaab$$aabab$
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196
Ullman (TOC) Edition 3 Exercise 7.3 Question 7 (Page No. 299)
Complete the proof of theorem $7.27$ by showing that $(q_{P},w,Z_{0})\vdash(q,\in,\gamma)$ if and only if $(q_{P},q_{A},w,Z_{0}) \vdash((q,p),\in,\gamma),$ where $p =\hat{\delta}(p_{A},w).$
Complete the proof of theorem $7.27$ by showing that$(q_{P},w,Z_{0})\vdash(q,\in,\gamma)$ if and only if $(q_{P},q_{A},w,Z_{0}) \vdash((q,p),\in,\gamma),$ where $p =\hat...
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200
Ullman (TOC) Edition 3 Exercise 7.3 Question 3 (Page No. 297)
Show that the $CFL's$ are not closed under the following operations$:$ $\text{min}$ $\text{max}$ $\text{half}$ $\text{alt}$
Show that the $CFL's$ are not closed under the following operations$:$$\text{min}$$\text{max}$$\text{half}$$\text{alt}$
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204
Ullman (TOC) Edition 3 Exercise 7.2 Question 4 (Page No. 287)
Use Ogden's lemma $($Question $2)$ to simplify the proof in example $7.21$ that $L=\{\text{ww|w is in $\{0,1\}^{*}$}\}$ is not a $CFL.$Hint$:$With $z=0^{n}1^{n}0^{n}1^{n},$ make the two middle blocks distinguished.
Use Ogden's lemma $($Question $2)$ to simplify the proof in example $7.21$ that $L=\{\text{ww|w is in $\{0,1\}^{*}$}\}$ is not a $CFL.$Hint$:$With $z=0^{n}1^{n}0^{n}1^{n}...
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