# Questions tagged [context-free]

Questions about the set of languages (equivalently) described by context-free grammars or accepted by (non-deterministic) pushdown automata.

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### 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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### 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 ...
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### 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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### 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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### 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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### 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:...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### (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 ...
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### 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 ...
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### Grammar for context free language

I want to give a grammar for the following language: $$L = \{x^r \# y |x, y \in \{a, b, c\}^*\\ \text{ and }x\text{ is a contiguous sub-string of }y\}$$ where $x ^ r$ denotes the backward written ...
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### Is this language L context-free?

The language $$L = \{x^r \# y | x, y \in \{a, b, c\}^*\\ \text{ and }x\text{ is a contiguous sub-string of }y\}$$ where $x ^ r$ denotes the backward written word x, is context-free. Can someone ...
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### Prove by Pumping Lemma that Language $L=\{a^ib^kc^k : i\geq k\geq 1\}$ isn't Context-Free

I'm new to this forum. I have some difficulties on using Pumping Lemma to prove non-CF language. Let $L=\{a^ib^kc^k : i\geq k\geq 1\}$ and the followings are my attempt. Proof. Suppose by ...
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### Does a Context-free language have a grammar that has either 3 or 0 nonterminals on the right hand side?

Is the following true or false? Why? Let L be a context-free language with $\epsilon\notin$ L. Then there is $\epsilon$-free grammar $G=(V,\Sigma, P,S )$ with $L (G) = L$, so all production rules are ...
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### Is this proof for showing that $EQ_{CFG}$ is co-Turing-recognizable incorrect?

I have been searching for proofs that show that $EQ_{CFG}$ is co-Turing-recognizable. When searching for proofs I can only find proofs on the following form: Construct a TM $M$ which recognizes the ...
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### Can the pumping lemma for context free languages be extended to any subword?

It is known that in the case of a Regular Language $L$ , the pumping lemma can be extended to apply to any sufficiently long subword of the language, ie, if $uwv \in L$ and $|w| \ge p$ then we can ...
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### Constructing CFG

How to generate CFG for this language? $L = \{ w \mid w \in \{ (, [, ], ) \}^* \text{ s.t. }$ In any prefix of $w$, no. of ( is more than no. of ), and no. of [ is more than no. of ]. $\}$ Thus,...
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### Decidability of $SEQ_{CFG} = \{⟨G,H⟩ \mid \text{$G,H$are CFGs and$L(G) ⊆ L(H)$}\}$

How can I prove that $SEQ_{CFG} = \{⟨G,H⟩ \mid \text{$G,H$are CFGs and$L(G) ⊆ L(H)$}\}$ is decidable ? I know that $EQ_{CFG} = \{⟨G, H⟩ \mid \text{$G,H$are CFGs and$L(G) = L(H)$}\}$ is not.
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### is $0^x1^y$ context-free?

given that L is regular, does the following make a context-free language?: i) $\{0^x1^y \mid 0^{x+y} \in L\}$ ii) $\{0^x1^y \mid 0^{x-y} \in L\}$ since L is regular, i presumed that i) can be put ...
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### Is the language $L$ of coded CFG's Turing decidable?

Consider the following language $L$ = {$<G><w>$ | $G$ is a CFG and $w\in L(G)$} Now, I wish to prove that $L$ is Turing decidable. My gut tells me to construct a Turing machine that ...
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### What's the right way to think about a CFG symbol with an infinite null derivation?

I'm curious about the right way to characterize symbol $A$ in a CFG like this one: \begin{align*} A &\to A B\\ A &\to x\\ B &\to y\\ B &\to \varepsilon \end{align*} $B$ is ...
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### If you have a smallest grammar approximation, do you immediately have a CFG inference algorithm?

The smallest grammar problem is to find a single-string CFG. So given a finite list of language samples, known to all lie in some CFG, can we, using the smallest grammars (approximated) of each ...
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### Give a Context Free Language, is the complement of this language always recursive(REC)?

I have seen some people make an argument that given the fact that Context Free Languages are proper subset of REC which is closed under complementation thus complement of a CFL must be in REC. I ...
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### How to construct Context Free Grammar of words with equal number of 0's and 1's [duplicate]

i am trying to find a cfg for this cfl L = $\{ w \mid w \text{ has an equal number of 0's and 1's} \}$ is there a way to count the number of 0's or 1's in the string?
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### Get grammar from his LALR(1) parsing table

I have a problem with this exercise. This is the LALR(1) parsing table for the grammar G. How can i get the productions of G? Thanks :)
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### SLR(1) Table construction, FIRST and FOLLOWS

when constructing the SLR(1) table for some grammar I need to compute the FOLLOW set for all terminals in order to decide where and when to reduce. Do I compute theme for the augmented grammar or ...
I was given the following grammar $S \rightarrow S ( S ) S\mid \epsilon$ First I was asked to eliminate left recursion, yielding me the following : $S \rightarrow S'$ \$S' \rightarrow (S)...