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Recent questions tagged context-free-grammars

0 votes
1 answer
1
Consider an $\varepsilon$-tree CFG. If for every pair of productions $A\rightarrow u$ and $A\rightarrow v$ If $\text{FIRST(u)} \cap \text{FIRST(v)}$ is empty then the CFG has to be $LL(1).$ If the CFG is $LL(1)$ then $\text{FIRST(u)} \cap \text{FIRST(v)}$ has to be empty. Both $(A)$ and $(B)$ None of the above
asked Apr 1, 2020 in Compiler Design Lakshman Patel RJIT 247 views
0 votes
1 answer
3
Let $G$ be a grammar in CFG and let $W_1,W_2\in L(G)$ such that $\mid W_1\mid=\mid W_2\mid$ then which of the following statements is true? Any derivation of $W_1$ has exactly the same number of steps as any derivation of $W_2$. Different derivation have different length. Some derivation of $W_1$ may be shorter than the derivation of $W_2$ None of the options
asked Mar 30, 2020 in Theory of Computation Lakshman Patel RJIT 289 views
0 votes
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5
Let $G= (V,T,S,P)$ be a context-free grammer such that every one of its productions is of the form $A\rightarrow v$, with $\mid v \mid=K> 1$. The derivation tree for any $W \in L(G)$ has a height $h$ ... $\log_{K}|W \mid \leq h \leq \left (\frac{ \mid W \mid - 1}{K-1} \right)$
asked Mar 24, 2020 in Theory of Computation jothee 173 views
1 vote
4 answers
6
The language which is generated by the grammar $S \rightarrow aSa \mid bSb \mid a \mid b$ over the alphabet of $\{a,b\}$ is the set of Strings that begin and end with the same symbol All odd and even length palindromes All odd length palindromes All even length palindromes
asked Jan 13, 2020 in Theory of Computation Satbir 321 views
3 votes
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7
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8
Prove that the following two languages are undecidable. $OVERLAP_{CFG} = \{\langle G, H\rangle \mid \text{G and H are CFGs where}\: L(G) \cap L(H) \neq \emptyset\}$. $PREFIX-FREE_{CFG} = \{\langle G \rangle \mid \text{G is a CFG where L(G) is prefix-free}\}$.
asked Oct 20, 2019 in Theory of Computation Lakshman Patel RJIT 134 views
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9
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12
Say that a variable $A$ in $CFL\: G$ is usable if it appears in some derivation of some string $w \in G$. Given a $CFG\: G$ and a variable $A$, consider the problem of testing whether $A$ is usable. Formulate this problem as a language and show that it is decidable.
asked Oct 17, 2019 in Theory of Computation Lakshman Patel RJIT 138 views
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13
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14
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15
If we disallow $\epsilon$-rules in CFGs, we can simplify the DK-test. In the simplified test,we only need to check that each of DK’s accept states has a single rule. Prove that a CFG without $\epsilon$-rules passes the simplified DK-test iff it is a DCFG.
asked Oct 13, 2019 in Theory of Computation Lakshman Patel RJIT 56 views
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16
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Let G be the following grammar: $S \rightarrow T\dashv $ $T \rightarrow T aT b \mid T bT a | \epsilon$ Show that $L(G) = \{w\dashv \: \mid w\: \text{contains equal numbers of a’s and b’s} \}$. Use a proof by induction on the length of $w$. Use the DK-test to show that G is a DCFG. Describe a DPDA that recognizes L(G).
asked Oct 13, 2019 in Theory of Computation Lakshman Patel RJIT 48 views
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20
Let $\Sigma = \{0,1\}$ and let $B$ be the collection of strings that contain at least one $1$ in their second half. In other words, $B = \{uv \mid u \in \Sigma^{\ast}, v \in \Sigma^{\ast}1\Sigma^{\ast}\: \text{and} \mid u \mid \geq \mid v \mid \}$. Give a PDA that recognizes $B$. Give a CFG that generates $B$.
asked Oct 13, 2019 in Theory of Computation Lakshman Patel RJIT 263 views
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21
Consider the following CFG $G:$ $S \rightarrow SS \mid T$ $T \rightarrow aT b \mid ab$ Describe $L(G)$ and show that $G$ is ambiguous. Give an unambiguous grammar $H$ where $L(H) = L(G)$ and sketch a proof that $H$ is unambiguous.
asked Oct 12, 2019 in Theory of Computation Lakshman Patel RJIT 144 views
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22
Show how, having filled in the table as in Question $4.4.9$, we can in $O(n)$ time recover a parse tree for $a_{1}a_{2}\cdot\cdot\cdot a_{n}$. Hint: modify the table so it records, for each nonterminal $A$ in each table entry $T_{ij}$, some pair of nonterminals in other table entries that justified putting $A$ in $T_{ij}$.
asked Aug 20, 2019 in Compiler Design Lakshman Patel RJIT 44 views
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23
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24
Design grammars for the following languages: The set of all strings of $0's$ and $1's$ such that every $0$ is immediately followed by at least one $1$. The set of all strings of $0's$ and $1's$ that are palindromes; that is, the string reads the same backward as forward. The set of all ... of all strings of $0's$ and $1's$ of the form $xy$, where $x\neq y$ and $x$ and $y$ are of the same length.
asked Aug 17, 2019 in Compiler Design Lakshman Patel RJIT 84 views
1 vote
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25
Repeat Question $4.2.1$ for each of the following grammars and strings: $S\rightarrow 0S1\mid 01$ with string $000111$. $S\rightarrow +SS\mid \ast SS\mid a$ with string $+\ast aaa$. $S\rightarrow S(S)S\mid \epsilon$ with string $(()())$ ... $bterm\:\rightarrow\:bterm\:and\:bfactor\mid bfactor$ $bfactor\:\rightarrow\:not\:bfactor\mid (bexpr)\mid true\mid false$
asked Aug 17, 2019 in Compiler Design Lakshman Patel RJIT 145 views
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