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22 votes
3 answers
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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 ...
Luke Mathieson's user avatar
15 votes
4 answers
5k views

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 ...
BlueBomber's user avatar
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13 votes
2 answers
4k views

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 ...
bongubj's user avatar
  • 563
12 votes
2 answers
591 views

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: ...
gewo's user avatar
  • 121
10 votes
1 answer
5k views

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 ...
Ivan Meza's user avatar
  • 103
10 votes
4 answers
795 views

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 $\...
rl1's user avatar
  • 243
9 votes
1 answer
5k views

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 ...
arty's user avatar
  • 193
9 votes
1 answer
760 views

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 ...
lukas.coenig's user avatar
9 votes
3 answers
1k views

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 \...
MrBolton's user avatar
8 votes
1 answer
598 views

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 ...
Romy's user avatar
  • 407
8 votes
1 answer
328 views

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 ...
haleh's user avatar
  • 151
7 votes
3 answers
3k views

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-...
User_1234's user avatar
  • 145
6 votes
1 answer
2k views

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 ...
Andrey Lebedev's user avatar
6 votes
1 answer
1k views

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 ...
Matheus Moreira's user avatar
6 votes
2 answers
198 views

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. ...
Andrey Lebedev's user avatar
5 votes
1 answer
1k views

Why can't linear bounded automata accept an empty string?

The linear bounded automata (LBA) is defined as follows: A linear bounded automata is a nondeterministic Turing machine $M=(Q,\Sigma,\Gamma,\delta,q_0,\square,F)$ (as in the definition of TM) with ...
Mahesha999's user avatar
  • 1,763
5 votes
1 answer
793 views

Examples of context sensitive syntactic constructs (statements)

So, I am implementing a context sensitive syntactic analyzator. It's kind of an experimantal thing and one of the things I need are usable syntactical contructs to test it on. For example, the ...
tedd's user avatar
  • 53
5 votes
2 answers
306 views

From context-free to context-sensitive

I have a context-free language $L(G)$. I'm reading in a book that $L(G') = L(G) - \{{\epsilon}\}$ is context-sensitive but I cannot find a proof or confirmation of this fact; moreover, in other texts ...
Crysis85's user avatar
  • 255
5 votes
1 answer
132 views

Mildly context-sensitive grammar

Consider a context-sensitive grammar $G$, such that all the productions of $G$ have the form $A\to \alpha$ or $Ab \to \alpha b$ (in other words, the left context is always empty and the right context ...
Ewan Delanoy's user avatar
5 votes
1 answer
1k views

Membership problem for context sensitive languages PSPACE-complete

I have read that the membership problem for CSL is PSPACE-complete but I couldn't find the proof anywhere. So I tried it myself. Let's mark the membership problem for CSL as MEM. First I have to ...
Dracke's user avatar
  • 153
4 votes
1 answer
239 views

Is every language in PTime also context-sensitive?

Context-sensitive languages are exactly those that can be recognised using linearly bounded automata, i.e., those in NSPACE(O($n$)). This subsumes all languages that can be recognised in linear time, ...
mak's user avatar
  • 205
4 votes
1 answer
60 views

How to make sense of this context-sensitive production in a textbook? (a typo perhaps?)

In Chapter 1 of Kenneth Slonneger and Barry L. Kurtz's Formal Syntax and Semantics of Programming Languages: A Laboratory Based Approach, an example of its production is given to illustrate the nature ...
Archy Will He 何魏奇's user avatar
4 votes
1 answer
314 views

Type inference in compiler is context sensitive?

Have read in Compiler textbook that type inference is context sensitive. Can anyone explain why is it so? This means that we need context sensitive grammar in semantic analysis phase of a compiler ...
user5507's user avatar
  • 2,191
4 votes
1 answer
110 views

Why are four context sensitive grammar (CSG) rules needed to represent AB -> CD?

In Wikipedia of Kuroda normal form, it says A straightforward technique attributed to György Révész transforms a grammar in Kuroda's form to Chomsky's CSG: AB → CD is replaced by four context-...
xskxzr's user avatar
  • 7,520
4 votes
1 answer
111 views

Are the set of all Bitcoin addresses a context-sensitive language?

This started with me trying to make a regex to accept Bitcoin addresses. However, I couldn't do it. That led me to think: "is the set of all possible Bitcoin addresses even a regular language&...
Nathan Lim's user avatar
4 votes
1 answer
75 views

Can you diagonalize a language out of CSL?

In recursion theory, it is possible to diagonalize a computable function out of the class of primitive recursive functions. Can you do the same with context-sensitive languages? I was thinking we ...
Hugolin Bergier's user avatar
4 votes
1 answer
276 views

Context-sensitive grammars for $a^ib^jc^{ij}$ and $a^ib^jc^{i^j}$

I would like to get some help for finding the context-sensitive grammar for the language: $$L_1=\{a^ib^jc^{ij} \mid i,j\geq 0\}.$$ To answer the question before it's written here, yes I've tried to ...
Wanderer's user avatar
  • 279
4 votes
1 answer
192 views

Is there a recommended process for designing CSGs (other than intuition)?

I understand the differences between Regular, Context-Free, and Context-Sensitive languages. Designing a Regular Grammar can be easier if you have a DFA. Designing a CFG isn't too hard for the ...
delrocco's user avatar
  • 207
3 votes
3 answers
180 views

How to give a context-sensitive grammar for a^nba^nba^nb?

I am struggling on this problem since days: $L = \{a^nba^nba^nb \mid n \in \Bbb N\}$. I have to give for this language a context-sensitive grammar.
Apfelsaft's user avatar
3 votes
1 answer
3k views

PDA for { xy : |x| = |y|, x ≠ y} from its grammar, and intuition behind it

I know the grammar for the language $\{ xy : |x| = |y|, x ≠ y \}$ if $\Sigma=\{a,b\}$: $$ \begin{align*} &S→AB∣BA \\ &A→a∣aAa∣aAb∣bAa∣bAb \\ &B→b∣aBa∣aBb∣bBa∣bBb \end{align*} $$ I ...
Pavan Kumar Munnam's user avatar
3 votes
1 answer
366 views

What is language of repeat(L) = {ww | w ∊ L}? [closed]

What is language of repeat(L) = {ww | w ∊ L} ? My try: I know it {ww | w ∊ (a,b)*} is context sensitive language. Here , what is meant by "repeat(L)" ? Can you explain it ? It is not a ...
Mithlesh Upadhyay's user avatar
3 votes
1 answer
67 views

Have non-regular language classes of infinite words been studied?

For regular languages we have $\omega$-regular languages which extend them to infinite words. Are there such extensions for CFG's, CSG's and recursively enumerable languages?
nikhil_vyas's user avatar
3 votes
1 answer
161 views

Closure of context-sensitive languages under inverse language substitution

We define language substitution for a Context-Sensitive Language (CSL) $S$ over an alphabet $\Sigma$ is a map from $\Sigma$ into CSL's, for example: $f(abc) = L_1(a) L_2(b) L_3(c)$ such that (I guess) ...
SeekingAMathGeekGirlfriend's user avatar
3 votes
1 answer
1k views

Which properties of context sensitive languages are decidable?

There are two context-sensitive languages, $L_1$ and $L_2$. Which of the following statements about them are decidable respectively undecidable? $L_1 = \emptyset$ $L_1 = \Sigma^*$ $L_1 \cap L_2 = \...
Bharat Kul Ratan's user avatar
3 votes
1 answer
2k views

Is this an example of a type-0 grammar that is not context-sensitive?

A type-0 grammar generates a recursively enumerable (RE) language. A RE language is also known as a semi-decidable language. A semi-decidable language is a particular kind of undecidable language: ...
Roger Costello's user avatar
3 votes
0 answers
112 views

Generating valid sentence with respect to attribute grammar

Given a context free grammar, both the algorithm for determining whether a given string is grammatical and the algorithm for producing a grammatical string in that language are well understood. To ...
lightning's user avatar
  • 225
3 votes
0 answers
210 views

Is there a grammar type for deterministic LBA?

Contextsensitive grammars define exactly the langauges acceptable by nondeterministic LBA. But how about deterministic LBA - is there a grammar type capturing exactly the languages acceptable by this ...
lukas.coenig's user avatar
2 votes
3 answers
524 views

concatenation of context sensitive and context-free is context sensitive or not?

Assume that $L_1$ is context sensitive language and $L_2$ is context free language, is the language $L_1 * L_2$ context-sensitive or not? I almost sure that is not, but can't prove it.
dor navon's user avatar
2 votes
1 answer
815 views

Demonstrating that for every monotonic grammar there is an equivalent context-sensitive grammar

I'm trying to understand the equivalence in expressive power of formal grammars whose rules take the form: $$ \alpha \rightarrow \beta $$ where $ |\alpha| \leq |\beta| $ (called a monotonic grammar), ...
BlueBomber's user avatar
  • 1,297
2 votes
2 answers
137 views

Context-sensitive grammar for function calls

Say we have context-free grammar for function declarations and calls (C-style) ...
Konstantin Vladimirov's user avatar
2 votes
1 answer
116 views

How can I show that this language is context sensitive?

I have this language $L=\{a^nb^nc^n,n\geq0\}$, I know this language is not context free, but I don't know how to show that it is context sensitive, do I have to use a PDA?
Cheia's user avatar
  • 37
2 votes
2 answers
2k views

Examples of Context-sensitive grammars which produces non-indexed language

Well known example of Context-sensitive grammar which produces language $\{a^nb^nc^n|n\geq 1\}$ is widely used in various papers. But actually, while this language is definitely context-sensitive, it ...
Andrey Lebedev's user avatar
2 votes
2 answers
783 views

Ambiguity vs. context-sensitivity

It is said that attributes supply some semantic information to the grammar. Meantime, the same attributes let you to resolve ambiguities. Text books agree that it is worth haveing a CF grammar which ...
Valentin Tihomirov's user avatar
2 votes
1 answer
21 views

Valid rules in CSG

In the book of Hopcroft-Ullman (the 1979 edition) there is a rule $Da\rightarrow aaD$ in the example of the CSL language $a^{2^i}$. Valid rules in CSG have the form $\alpha A \beta\rightarrow \alpha\...
Ricardo Wehbe's user avatar
2 votes
1 answer
4k views

Difference between linear bound automata and a Turing machine

Can anyone give an example where a language can be rejected by linear bounded automata and accepted by a Turing machine. Is there any proof that a linear bounded automata is less powerful than a ...
Vamsi Shankar's user avatar
2 votes
1 answer
88 views

Show that $L:=\{(a^{k}b)^{i}|i,k \epsilon \mathbb{N}_{+} \}$ is context-sensitve. (With context-sensitive/noncontracting grammar)

I am studying for an upcoming exam and this is an old exam question from two years ago (all exams were made available through our lecturer): Show that $L:=\{(a^{k}b)^{i}|i,k \epsilon \mathbb{N}_{+} \}...
Edmundo Del Gusto's user avatar
2 votes
1 answer
229 views

What kind of languages can be recognized by a restricted one-tape deterministic Turing Machine?

During a lesson, our TA asked: What kind of languages can be recognized by a deterministic Turing Machine such that we can use only a tape portion that contains the input? My thoughts: my ...
Jack's user avatar
  • 175
2 votes
1 answer
177 views

An example of a context-sensitive grammar for a given language

Consider this language: $L = \{a^nb^ma^nb^m \mid n,m \ge 1\}$. Can we give for this language a context-sensitive grammar?
Apfelsaft's user avatar
2 votes
0 answers
61 views

Intuition on what an attribute grammar can achieve

I have seen attribute grammars for a small handful of tasks: Parsing simple arithmetical expressions Type checking Checking that a variable is initialized anbncn (seems to be a favorite toy example).....
lightning's user avatar
  • 225
2 votes
0 answers
277 views

Context-sensitive grammar for language $L = \left\{ww \mid w \in \left\{a,b\right\}^* \right\}$ [duplicate]

Find a context-sensitive grammar for language $L = \left\{ww \mid w \in \left\{a,b\right\}^* \right\}$ where $L \in DCSL \setminus CFL$. I find this task from old exam but there is no solution. I try ...
eyesima's user avatar
  • 121