# Tagged Questions

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2answers
113 views

### Known and described subclasses of Context-Free Grammars class

I'm looking for various researches which consider specific subclasses of Context-Free Grammar class, i.e. some specific described cases, which differ from well-known: deterministic/non-deterministic ...
0answers
67 views

### 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 ...
1answer
61 views

### In what way are these two context free grammar equal? [closed]

Consider the grammar G1: A->Aα|β G2: A->βX X->αX|ϵ Its was said that these two grammars are equal. Should something like left recursion be removed? In what sense are these equal? Am really ...
2answers
112 views

### Finding a minimal context free grammar that recognizes a finite set of strings of bounded length

Problem: Given a finite set of strings $\{x_1, x_2, ..., x_n\}$ of length $\ell$ or less from some finite alphabet $\Sigma=\{a_1, a_2, ..., a_k\}$, find the minimal context free grammar that ...
3answers
189 views

### Does there exist a hardest DCFL?

Greibach famously defined a language $H$, the so-called nondeterministic version of $D_2$, such that any CFL is an inverse morphic image of $H$. Does there exist a similar statement with DCFL, ...
0answers
177 views

### 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. ...
0answers
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### Difference between 'string relations' and 'tree relations' w.r.t. synchronous CFGs

Context: http://www3.nd.edu/~dchiang/papers/synchtut.pdf On page 3, under the section Properties, at the end of the paragraph labeled Closure under composition?, the author mentions 'tree relations ...
0answers
63 views

### Counting words of length $n$ in an inherently ambiguous CFG?

There is a polynomial-time algorithm for computing the number of words of length $n$ in an unambiguous CFG $G = (V, \Sigma, R, S)$ (via a dynamic programming approach). However, for ambiguous CFGs, ...
1answer
60 views

### Can context-free grammar generates $a^{2^n}$ [closed]

Context-free grammar can generate the string $a^{2^n}$ for $n \geq 0$. The production rule P is $S \rightarrow SS | a$. The derivations is, for example: 1) $S \Rightarrow a$ (this is when n = 0) 2)...
0answers
83 views

### Chomsky-Schützenberger for Deterministic CFLs

Is there a Chomsky-Schützenberger representation theorem for deterministic CFLs? Knowing precisely the class of morphisms under which DCFL is closed, such a theorem would probably be of the form: ...
1answer
185 views

0answers
128 views