In formal language theory, a context-free language (CFL) is a language generated by some context-free grammar (CFG). The set of regular languages is a subset of the set of context-free languages.
Questions tagged [context-free-language]
183 questions
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Constructing a CFG
I literally can't find the answer to this:
L = {vw | v element of {a,b), w element of {b,c}, number of a's <= number of c's}
V --> aV | bV | e
W --> bW | cW | e
But I cannot think of how to combine the construction of the words v and w after one…
user3394178
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Pumping Lemma for CFL a^n b^m c^o for n
Let be: L={an bm co | n < m < o, n natural}
Using Pumping Lemma I have choosen: z = uvwxy = an bn+1 cn+2
|uv|<=n and |v|>0
=> uv2wx2y
If vwx is of a's and / or b's it is okay and we would have more a's and/or b's than c's - but if vwx contains only…
paulgavrikov
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Language accepted PDA
Suppose we have the following PDA: M=
delta(q0, 1, $) = {(q0, X$)}
delta(q0,λ, $) = {(q0, λ)}
delta(q0, 1, X) = {(q0, XX)}
delta(q1, 1, X) = {(q1, λ)}
delta(q0, 0, X) = {(q1, X)}
delta(q1, 0, $) = {(q0, $)}
my…
Ziyad Mestour
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Unambiguous Context free Grammar
I was reading through Context Free Grammar, and I came across ambiguous grammar. If the language produced by CFG has more then 1 parse tree, then CFG is an ambiguous grammar.
Is there any way by which I can find out or prove that the grammar is…
meow
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Context-free language not closed under intersection
I found this solution on Wikipedia. Shouldn't it say: j>n≥ 0
Because the intersection are elements that are common in both languages.
Consider the languages L1 and L2 defined by L1={a^(n)b^(n)c^(j)| n,j ≥ 0} and L2 = {a^(j)b^(n)c^(n): n,j ≥ 0}.…
Jonathan Lam
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Is the language L = { a^n b^j : j ≤ n ≤ 2j − 1 } context-free?
Is the language L = { anbj : j ≤ n ≤ 2j − 1 } context-free?
I have no idea how to start with this exercise. I am familiar with the pumping lemma, but I have no idea how I should use it here. It seems to me that this language is context-free and that…
Ronald
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CFG for a = b and c = d (length)
I know how to construct the context-free grammars for strings that have same counts of a and b, or have the same counts of c and d:
S → ε S → ε
S → SASBS S → SCSDS
S → SBSAS S → SDSCS
A → a C → c
B → b …
leander
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converting CFG to regular expression
Here's a CFG that generates strings of 0s, 1s, or 0s and 1s arranged like this (001, 011) where one of the characters must have a bigger count than the other like in 00011111 or 00000111 for example.
S → 0S1 | 0A | 0 | 1B | 1
A → 0A | 0
B → 1B |…
Sieg
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What makes this example a context-free language rather than regular language?
I'm having trouble seeing what makes "any number of a's followed by the same number of b's and c's" a context-free language, while "any number of a's followed by any number of b's followed by any number of c's" is a regular language, as I saw…
sonder
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How to remove left recursion from A -> Aα | ε
I think the left-recursion for this grammar is not removable. Correct me if I am wrong.
α is Alpha that is a Non-terminal
ε is Epsilon.
HamzaFarooq
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Need help in generating a CFG for a language
I want to match strings that contain "k" number of 0's followed by "k+4" number of 1's where k is greater than or equal to zero
I tried the following grammar is this correct?
S->0S1|1111
mike
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Make a grammar unambiguous?
I have the following problem. This grammar is ambiguous:
stmt -> if expr then stmt stmt’ | a
stmt’ -> else stmt | EPSILON
expr -> b
I tried to modify it and my result is:
stmt -> if expr then stmt’’ | a
stmt’’ -> stmt | stmt’
stmt’ -> B else…
thommyho
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One Language and Proof How it's ambiguous?
I just took my midterm but couldn't answer this question.
How we can show the following language is ambiguous ?
L={a n bm c p : n≠m} U {a n
bm c p : m≠p}
I think this is very hard, Who can Help me with automated tools or ... how we can…
user4249446
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1 answer
Determine if a language is context free
Lets say you have a language L and you want to determine if it is context free. Context free languages intersected with regular languages are context free. Is that enough to prove that L is context free?
Meaning,
L intersect P = T Where P is a…
John Smith
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CFG and DCFG Decidable problems
Can you guys list the problems that you are aware that are decidable for Context free Language and for Deterministic Context free languages. I did get some info on list of undecidable problems on Stack Overflow and Wiki, but not related to CFG or…
Nikhil Mahajan
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