All Questions
Tagged with context-free grammars
11 questions with no upvoted or accepted answers
10
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0
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254
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Smallest context-free grammar for powers of two summing to $2^k$
Let $k > 0$ and define an alphabet $\Sigma_k = \{ 2^0, 2^1, \ldots, 2^k \}$. Define:
$$P_k = \{ a_1a_2\cdots a_t \in \Sigma_k^* \mid \sum_i a_i = 2^k \}.$$
This is a finite language.
Question: Is ...
- 3,976
10
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274
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Complexity of a problem over acyclic context-free grammars
Let $G$ be an acyclic, context-free grammar over a fixed alphabet $\Sigma=\{a_1,\dots,a_k\}$ with the restriction (without loss of generality) that $|w|=2$ for each rule $A\to w$ in the grammar. ...
- 500
7
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845
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Does PEG contain CFG?
Despite their considerable expressive power, all PEGs can be parsed in linear time using a tabular or memoizing parser (8). These properties strongly suggest that CFGs and PEGs define incomparable ...
- 420
5
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164
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"Context" understanding in tree grammars
The Context-Free tree grammar has rules of the form:
$A\rightarrow t$ or $A(x_1,\dots,x_n)\rightarrow t_x$,
where $A\in N$, $t\in T(N\cup T)$, $t_x\in T(N\cup T\cup \{x_1,\dots,x_n\})$, $T(Z)$ ...
- 635
3
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0
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164
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Deciding whether an arbitrary context-free grammar generates a deterministic push-down automata?
I know that it's undecidable whether an arbitrary context-free grammar is ambiguous, but is it decidable whether that grammar is deterministic? I can't find the answer to this question anywhere on the ...
- 131
3
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0
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178
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Context-Sensitive Grammar characteristic properties
This question can look like some kind of puzzle, but it is actually part of more complex applied problem.
Let's consider subspace of Context-Sensitive Grammars, which contains grammars which can not ...
- 635
2
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0
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76
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A Context-Sensitive Grammar which cannot be recognised by a Parsing Expression Grammar
It is (currently) an open question of whether every context-free grammar can be recognised by some parsing expression grammar. [1]
However, has it been proven that there exists an example of a ...
- 121
2
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0
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249
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Structural equivalence of two context-free grammars
I understand that determining if two context-free grammars are structurally equivalent is decidable (according to the 1968 paper by Paull, M.C. and Unger, S.H., "Structural equivalence of context-free ...
- 63
1
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What is the interpretation of an infinite formal context-free grammar?
Let $L$ be a language as follows:
$$
\begin{align*}
L &::= a\ |\ L^{*}\\
\end{align*}
$$
Now, suppose I apply some sort of transformation $T : N \rightarrow N$ where $N$ is the set of non-...
- 309
0
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0
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39
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Are there approaches to deriving a Grammar(production rules) from given set of strings?
Apologies for unambiguous question. So far I have a lot of difficulties of discerning on how to design formal production rules for some formal language aside from classic examples such as equal pairs ...
- 9
0
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Are there data structures that cannot be serialized / deserialized using a context free grammar?
I understand that deserializing data from a string or binary stream into a data structure is effectively the same parsing. When you deserialize the input string, you use a grammar to create a parse ...
