Questions tagged [context-free]
Questions about the set of languages (equivalently) described by context-free grammars or accepted by (non-deterministic) pushdown automata.
1,191
questions
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How to prove that a language is not context-free using pumping lemma
I'm trying to prove that that language isn't a context free:
$ L = \{ w11w \mid w\in \Sigma^* = \{0,1\}\}$
I succeed to prove that $L = ww$ isn't context free, but not the language above. What ...
0
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0answers
40 views
Find PDA for CFL = {x#y | |x| = |y| and x ≠ y} [duplicate]
I am studying push down automata.
When I read a solution for showing $L = \{x\#y \mid x \neq y, x,y \in \{0,1\}^*\}$ is a CFL, I could understand $L = L_1 \cup L_2$, $L_1 = \{x\#y\mid|x| \neq |y|\}$, ...
1
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1answer
57 views
Creating a CFG from a specific CFL
I am pretty desperate finding the correct context free grammar for the following language:
$$L=\{a^lb^mc^n \mid l,m,n \in \mathbb{N}_0, \, l\geq 2n+m\}$$
I would really appreciate if anyone could ...
0
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0answers
23 views
About Specification of PDA
I was learned NPDA is specified by a tuple $P = (Q,\Sigma,\Gamma,\delta,q_0,Z_0,F) $,
$Q$ is a finite set of states
$\Sigma$ is a finite set of input symbols (input alphabet)
$\Gamma$ is a finite ...
1
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1answer
48 views
Proving that the set of grammars generating L or L complement is undecidable
Let $X$ be a regular language, I need to prove that either $\{G \mid L(G) = X\}$ or $\{G \mid L(G) = \overline{X} \}$ is undecidable using the following hint: Use reduction to absurdity supposing that ...
1
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1answer
37 views
Undecidability of checking whether all words can be generated from a context-free grammar?
I know it's undecidable, but how to prove it?
Let me explain the problem clearer. The problem is not to check whether some given word can be generated, but whether ALL words are possible to generate ...
3
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1answer
57 views
Is there an algorithm to overapproximate a context free grammar by a regular expression?
I understand that a context-free grammar is strictly powerful than a regular expression in that a context free grammar can represent any regular language, but not all context free languages can be ...
0
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2answers
422 views
Convert this language to Context Free Grammar
I'm having trouble understanding how to convert this language to context free grammar.
$\{a^ib^jc^k\mid i > k, 0\le j \lt3, k \ge 0\}$
Part im getting stuck on is how to deal with a and c, ...
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2answers
568 views
CFG for L {a^nb^m | n <= m+3}
I need a Context Free Grammar for this language. I could come up with this solution:
S -> AB
A -> aA | ε
B -> bbbB | ε
But, this grammar is clearly ...
0
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2answers
197 views
CFG for the language L ={a^n w | w \in {b,c}^*, n= count of b.c in w. }
$L =\{a^nw \mid w \in \{b,c\}^*$, $n=$ #$_b$ + #$_c$$\}$
$\bullet $ #$_b$ denotes the number of $b$'s in $w$
$\bullet $ #$_c$ denotes the number of $c$'s in $w$
I have some trouble designing a CFG ...
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1answer
169 views
Constructing PDA to accept language { 0^i 1^j 2^k | i = 2j or i = k, where i,j,k >= 1 }
$L = \{ 0^i 1^j 2^k \mid i = 2j \text{ or } i = k, \text{ where } i,j,k \geq 1 \}$
I have trouble about this PDA. Anybody can help me about draw this PDA?
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0answers
35 views
Is there any grammar parseable by LALR(1) but not LR(1)?
https://en.wikipedia.org/wiki/LALR_parser - as far as I understand, LALR(1) is a simplified version of LR(1), aiming to achieve a greater parsing performance at the expense of reduced power. So, IIUC, ...
0
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1answer
50 views
What are the sufficient conditions for a grammar to be unambiguous?
There is no algorithm that, given an arbitrary grammar, decides if it's ambiguous or not. However, Are there any sufficient conditions that make it easier to tell that a grammar is unambiguous?
For ...
2
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2answers
61 views
Operator name in LL(1) computation
I'm working from a definition of the LL(1) property of context-free languages in order to build a LL(1)-computer, i.e., a program capable of determining whether a given context-free language is in LL(...
0
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0answers
247 views
a^nb^nc^nd^n using 2-stack PDA
I need to construct a PDA using 2 stacks for accepting the language $L = \{a^nb^nc^nd^n | $ $n \geq 0\}$.
Pushing $a$'s to first stack and $b$'s to second and poping them for corresponding $c$'s and ...
2
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2answers
52 views
Why can we (apparently) implement CFG parsers only using (N)DFAs?
I am working on a project in which I need to parse files written in different DSLs. One important feature of these languages is that most of them allow blocks to be nested.
For parsing those files I ...
1
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1answer
243 views
Binary strings such that the sum of 0's is not equal to twice the sum of 1's
Construct a context-free language for $L=\{w\in \{0,1\}^* \mid n_0(w)\not= 2n_1(w)\}$. Here $n_b(w)$ is the number of $b$'s in $w$.
I can construct a CFL in the case $n_0(w)=2n_1(w)$, but I have no ...
2
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1answer
99 views
Finding an unambiguous grammar of a language provided by a CFG
I'm working through 'Intro to Automata Theory, Language and Computation' 2nd edition by Hopcroft, Motwani & Ullman.
In section 5.4, exercise 5.4.3 I am tasked with finding an unambiguous grammar ...
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2answers
114 views
How do I model line comments in a CFG?
Assume we want to define a context free grammar of say a programming language, where on each line everything after the character # until the end of line is considered a comment and should be ignored. ...
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0answers
87 views
Accounting for spaces in grammars
Sometimes in a context free language we'd like to require spaces between productions, and sometimes not. For example take the following part from a grammar describing grammars:
...
1
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1answer
51 views
Can the complement of a context-free language be regular?
I know that the context-free language is not closed under the complement ,
and the result could be context-free language or non-context free language
but my question is :
is it possible of the ...
2
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1answer
34 views
Equivalent unambiguous grammar
Given the grammar:
$S \to AS\mid \varepsilon$
$A \to A1\mid 0A1 \mid \varepsilon$
Generate a new unambiguous grammar that generates the same language as the grammar above.
I have no idea how to ...
1
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2answers
38 views
Proving that a specific grammar is ambiguous
How can I prove that the following grammar is ambiguous:
$$ A \to AA\mid B \\ B \to aBb\mid ab $$
I tried finding a string that can be derived in two different ways, but to no avail.
0
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1answer
51 views
Crafting a Context Free Grammar
I'm trying to figure out the intuition on creating a CFG in my head. I understand the idea of Grammar rules akin to "onions" with various layers throughout. For example, I was working on a problem ...
2
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3answers
55 views
When are two CFG's different?
If two CFG's differ only in what names they use for their non-terminals, are they different?
For example, are these CFG's different:
$$\begin{align*}
S &\to A \\
A &\to a \end{align*}$$
and
$...
2
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1answer
86 views
The language $\{ww \mid w \in \{0,1\}^{*} \}$ is not a CFL
We have proved that the language $ L = \{\omega\omega \mid \omega \in \{0,1\}^{*} \} $ is not a CFL, and we did so by using pumping lemma. And the proof is clear to me. But I thought of the following ...
1
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1answer
326 views
Language whose intersection with a CFL is always a CFL
Prove or disprove: If the language $L$ is such that for every context-free language $L_0$, the language $L \cap L_0$ is context-free, then $L$ is regular.
I haven't managed to prove this, but I'm ...
0
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1answer
58 views
Finding a mapping reduction from $A_{TM}$ to $\overline{CF_{TM}}$
I am trying to find a mapping reduction from $A_{TM}$ to $\overline{CF_{TM}}$, but I can't seem to find one.
Definitions:
$$\begin{align*}
CF_{TM} &= \left\{ \langle M \rangle \mid \text{$M$ is a ...
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1answer
74 views
Context Sensitive Grammar for the language $\{a^n b^n c^{2+k}\mid n \ge 1, 0 \le k\le 1\}$ [closed]
I'm studying for my final exam and come up with this exercise with no idea how to find the production rule of this grammar.
I need help. Thanks all of you! :)
1
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1answer
35 views
Is substitution done to all occurrences?
In a CFG, we might have :$A \rightarrow AA$ and $A \rightarrow a$ where $a$ is a terminal and $A$ is a variable.
Then if we apply the first rule, and then the second , do we get $aa$ or either $aA$ ...
2
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3answers
91 views
Are $CF_{TM}$, $\space $ $\overline{CF_{TM}}$ Turing-recognizable?
I have searched the site well through, and also using Google and notes and couldn't find an answer to a question I am wondering about.
Given:
$$CF_{TM} =\{ \langle M \rangle \mid \text{$M$ is a TM ...
2
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0answers
31 views
Generating context-free grammar from language [duplicate]
I need to give a context-free grammar for each of the examples:
$L_1=\{a^hb^ka^mb^n : h+k=m+n\}$
$L_2=\{a^ib^ja^k : (i=j \,\,\,\, and \,\,\,\, k≥0) \,\,\,\, or \,\,\,\, (i\ge0 \,\,\,\, and \,\,\...
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0answers
32 views
How to make the length even for the words whose number of 0s is double its number of 1s? [duplicate]
How do I make a context-free grammar (CFG) for the following language?
$$L = \{w \in \{0, 1\}^* : \#_0(w) = 2\#_1(w)\text{ and } |w|\text{ is even}\}.$$ I have
$$S \to S1S0S0S \mid S0S1S0S \mid ...
1
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1answer
242 views
For any two regular languages A, B, show that {xy|x ∈ A, y ∈ B, |x| = |y|} is context-free
Basically I'm wondering if the concatenation of two equal length string is context free. I've seen multiple proofs of this online using PDAs but we aren't covering them in my automata course and my ...
5
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1answer
150 views
Is a kind of reverse Kleene star of a context-free language context-free?
Recently I had a question on one of my assignments asking to prove or disprove the following:
Let $L$ be a language. If $L^*$ is context-free then $L$ is context-free.
Now obviously this is false ...
1
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1answer
97 views
Proving that L(G) is the language defined by the CFG G
I have a context-free grammar defined by the production S:
S → aSbS ∣ bSaS ∣ ε
I need to prove that the CFG "G" can be defined as a language L(G) where
L(G) = {w ∈ {a, b}∗ ∶ na(w) = nb(w)}.
...
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0answers
71 views
How to generate random strings from Context-Free Grammar in GNF
I need to generate random strings given a grammar in Greibach Normal Form.
The naive approach would be to generate a random integer n and perform ...
0
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1answer
48 views
Context free grammar for L={ ((ab)^n)^m }
I want to write a cfg for the following language:
$ L = {((ab)^n)^m }$ $m,n >= 0$
this language produces (abababababab) where: $n=2, m=3 \\ or \\ n=3, m=2$
I have no idea what to do with it!
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2answers
736 views
Language involving irrational number is not a CFL
I am working through a hard exercise in a textbook, and I just can't figure out how to proceed. Here is the problem. Suppose we have the language $L = \{a^ib^j: i \leq j \gamma, i\geq 0, j\geq 1\}$ ...
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0answers
70 views
Proving the Complement of a DCFL is DCFL [duplicate]
If I Have a DCFL $L$ ( a CFL which can be recognised by a DPDA ),
How do I prove that $\overline{L}$ is also a DCFL
I checked my textbook for a proof but I wasn't able to understand the language.
Can ...
0
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0answers
38 views
construct regular expression for a language [duplicate]
I want a regular expression for the following language.
(a+b+c)*, but does not contain substring "abab".
That means it can be any combination of (a, b, c) except "abab".
I tryed to construct it ...
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2answers
82 views
What is the language L, generated by the grammar G?
Given the grammar $G = (Ν, Σ, Π, S)$, where $Ν = \{S\}$, $Σ = \{0, 1\}$, $Π = \{S → ε, S → 0, S → 1, S → 0S0, S → 1S1\}$, and $S$ is $S$. What is the language generated by the grammar?
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1answer
99 views
Find a CFG for $\{a^ib^jc^k \mid i,j,k\ge0 , \text{if } j=1 \text{ then } i=k\}$
I've tried but I can't figure out any solution. Is there any hint for me to solve the question?
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1answer
45 views
Is this language is Context-free language or not?
Is anybody can help me please to determine is this language is Context-free language or not?
L={wvw | w,v∈{a,b,c}+}
for example:
part of the language: acbac, abcab, bbcbb
not part of the language:...
1
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1answer
118 views
How to find First in a left recursive grammar?
One of the basic requirements for a grammar to be LL(1) is : For every pai r of productions A -> X | Y, First(X) and First(Y) should be disjointed.
If a grammar is left-recursive, then the set of ...
3
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1answer
52 views
Create a grammar that generate the language a^n . b^m . c^q . d^p such that n + p = q + m
I'm stuck on this question. I'm struggling on how to keep track of the number of a and d I have generated.
The professor hasn't given the correction.
I have seen similar questions but the condition ...
1
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1answer
44 views
Is λ allowed in Deterministic CFG?
I have a non-deterministic CFG that says
S-> aS | aB | bB | λ;
B-> bB | λ
And I'm asked to create a deterministic CFG from that. I understand why the given CFG is non-deterministic because it ...
1
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1answer
47 views
Whether it's necessary for a grammar to be ambiguous when it is both left recursive and right recursive
I read somewhere that if a grammar is left recursive as well as right recursive, then it is not necessarily ambiguous.
I couldn't make up my mind on this statement. How can a grammar which is both ...
1
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0answers
22 views
(Non) Context Free Language…? [duplicate]
I hope you could help me as you have done before (thanks again)
In a previous exam I saw this question; it is asked to identify if the language is Regular, CFL or Non CFL.
In my opinion this ...
0
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0answers
148 views
The rightmost derivation is possible with the same rule of leftmost derivation
Can someone please help me in understanding the statement. What does it exactly mean?
What I think it means is that:
the derivation produces by the leftmost derivation is also possible with rightmost ...
