Questions tagged [formal-grammars]

Questions about formal grammars, generative descriptions of formal languages.

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15 votes
2 answers
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Are the Before and After sets for context-free grammars always context-free?

Let $G$ be a context-free grammar. A string of terminals and nonterminals of $G$ is said to be a sentential form of $G$ if you can obtain it by applying productions of $G$ zero or more times to the ...
Alex ten Brink's user avatar
11 votes
2 answers
6k views

How can I prove this language is not context-free?

I have the following language $\qquad \{0^i 1^j 2^k \mid 0 \leq i \leq j \leq k\}$ I am trying to determine which Chomsky language class it fits into. I can see how it could be made using a context-...
justausr's user avatar
  • 435
6 votes
1 answer
1k views

Can every linear grammar be converted to Greibach form?

Can every linear grammar be converted to a linear Greibach normal form, a form in which all productions look like $A \rightarrow ax$ where $a \in T$ and $x \in V \cup \{\lambda\}$? ($T$ is the set of ...
Gigili's user avatar
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10 votes
1 answer
483 views

Given a string and a CFG, what characters can follow the string (in the sentential forms of the CFG)?

Let $\Sigma$ be the set of terminal and $N$ the set of non-terminal symbols of some context-free grammar $G$. Say I have a string $a \in (\Sigma \cup N)^+$ such that $x a y \in \mathcal{S}(G)$ where $...
Thomas's user avatar
  • 203
17 votes
3 answers
3k views

Decidable non-context-sensitive languages

It is arguable that most languages created to describe everyday problems are context-sensitives. In the other hand, it is possible and not hard to find some languages that are not recursive or even ...
Victor Stafusa - BozoNaCadeia's user avatar
40 votes
2 answers
6k views

Are there inherently ambiguous and deterministic context-free languages?

Let us call a context-free language deterministic if and only if it can be accepted by a deterministic push-down automaton, and nondeterministic otherwise. Let us call a context-free language ...
Patrick87's user avatar
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23 votes
1 answer
420 views

Is there any nongeneral CFG parsing algorithm that recognises EPAL?

EPAL, the language of even palindromes, is defined as the language generated by the following unambiguous context-free grammar: $S \rightarrow a a$ $S \rightarrow b b$ $S \rightarrow a S a$ $S \...
Alex ten Brink's user avatar
76 votes
1 answer
16k views

Language theoretic comparison of LL and LR grammars

People often say that LR(k) parsers are more powerful than LL(k) parsers. These statements are vague most of the time; in particular, should we compare the classes for a fixed $k$ or the union over ...
Raphael's user avatar
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35 votes
9 answers
5k views

What is the significance of context-sensitive (Type 1) languages?

Seeing that in the Chomsky Hierarchy Type 3 languages can be recognised by a state machine with no external memory (i.e., a finite automaton), Type 2 by a state machine with a single stack (i.e. a ...
bitmask's user avatar
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7 votes
1 answer
691 views

How to convert a non-embedding context free grammar to regular grammar?

A context-free grammar is said to be self-embedding if and only if contains a derivation of the form $\xi\stackrel*\Rightarrow u\xi v$, where $\xi$ is a non-terminal and $u$, $v$ are some non-empty ...
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