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Questions tagged [context-sensitive]

112 questions
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3 answers

Machines for context-free languages which gain no extra power from nondeterminism

When considering machine models of computation, the Chomsky hierarchy is normally characterised by (in order), finite automata, push-down automata, linear bound automata and Turing Machines. For the first and last levels1 (regular languages and…
Luke Mathieson
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Can someone give a simple but non-toy example of a context-sensitive grammar?

I'm trying to understand context-sensitive grammars. I understand why languages like $\{ww \mid w \in A^*\}$ $\{a^n b^n c^n \mid n\in\mathbb{N}\}$ are not context free, but what I'd like to know if a language similar to the untyped lambda…
BlueBomber
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Are all context-sensitive languages decidable?

I was going through the Wikipedia definition of context-sensitive language and I found this: Each category of languages is a proper subset of the category directly above it. Any automaton and any grammar in each category has an equivalent automaton…
bongubj
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What is the closure of context-free languages under finite intersections?

Famously the intersection of context-free languages need not be context-free. On the other hand the intersection of context-sensitive languages is context-sensitive. So this leads to the question: what is the closure of context-free languages under…
gewo
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A language in NSPACE(O(n)) and very likely not in DSPACE(O(n))

Actually I found that the set of context-sensitive Languages, $\mathbf{CSL}$ ($\mathbf{=NSPACE(O(n)) = LBA}$ accepted languages) are not so widely discussed as $\mathbf{REG}$ (regular languages) or $\mathbf{CFL}$ (context-free languages). And also…
rl1
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Is there an example of a recursive language which is not context sensitive?

I have been looking for a prototypical language for recursive languages (decidible) which is no context sensitive without success. For instance $a^*$ is prototypical of regular languages, $a^nb^n$ for context free languages and $a^nb^nc^n$ for…
Ivan Meza
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Can there be a context-sensitive pumping lemma?

A "pumping" property (words of a certain length imply the existence of loops in the language-defining mechanism) are known to exist for regular and context-free languages and a few more (usually used to disprove a language's membership to a certain…
lukas.coenig
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How to prove that context sensitive languages are closed under intersection and complement?

This is a question from the exam of our "Automata and Formal Languages" course. There is a question where asked to prove or disprove that any "relative complement" operation between two context sensitive languages will also produce a context…
arty
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Context-sensitive grammar for the language of words concatenated with themselves

I'm looking for a context-sensitive grammar that describes the following language: $L = \{ ww \mid w ∈ \{a,b\}^{\ast}, |w| ≥ 1\}$ . I've got problems with the fact that no rules such as $X \to \varepsilon$ are allowed and therefore I can't place…
MrBolton
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Is unary language with polynomial power context sensitive?

I suppose that $\Sigma = \{a\}$. Prove or Disprove: For every polynomial $p(n)$ with coefficients in $\mathbb{N}$, $L = \{a^{p(n)} \; | \; n \in \mathbb{N}\}$ is a context sensitive language. It seems that it is a context sensitive language. I guess…
haleh
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Class of the language only containing the empty string?

$L = \left \{ \epsilon \right \}$ Clearly this language is finite so this must be a regular language. Now since every regular language is Context Sensitive, $L$ is a CSL. We can define the grammar for $L$ as : $S\rightarrow \epsilon$ Now since $L$…
Romy
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What would a formal grammar for a binary file format look like?

Binary structures often feature length specifiers; the parser is supposed to read them and then consume the specified amount of symbols. Because of this, the grammar is context-sensitive. What would a context-sensitve grammar for a simple binary…
Matheus Moreira
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How to generate a context sensitive grammar for www

I am trying to solve for my exam coming up and have no clue how to generate the grammar for Context sensitive languages for example how do i proceed on this kind of question. Give a context-sensitive (not just length-increasing) grammar for $\{www…
User_1234
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A push-down automaton with two stacks which is equivalent to a linear-bounded automaton

It is known that a PDA with two stacks is equivalent to a TM. On the other hand a PDA with one stack is capable to recognise only context-free languages. Hence there is a kind of a gap between the class of PDA with one stack and the class of PDA…
Andrey Lebedev
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Context-sensitive grammars without permutation rules

Permutation rules are called those which are of the form $AB\Rightarrow^*BA$1. It is also proven that permutation rules expand context-free grammars and allow them produce non-context-free languages. My question is: are any examples of…
Andrey Lebedev
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