Linked Questions

3
votes
2answers
2k views

Proving that a word is *not* generated by a context-free grammar

I saw the answer in one of the solutions and I cannot figure out how they got the answer. The question is asked if the word is in the language or not for CNF... How did they get the answer so that ab ...
4
votes
2answers
6k views

Defining a context-free grammar for $\{w \in \{0, 1\}^* : \#_0(w) = \#_1(w)\}$ [duplicate]

I have a language where each string in the language has even amount of $0$'s as $1$'s (e.g., $0101$, $1010$, $1100$, $0011$, $10$ are all in the language). I was hoping to define a context-free ...
2
votes
2answers
69 views

Interpreting a Language

I'm having trouble understanding some language notation, primarily what rules I can take away from it. The language is as follows: $\qquad L = \{a^n b^m b^p c^p b^{n-m} \mid n > 0, m < n, p >...
26
votes
2answers
32k views

How to prove that a language is context-free?

There are many techniques to prove that a language is not context-free, but how do I prove that a language is context-free? What techniques are there to prove this? Obviously, one way is to exhibit ...
0
votes
1answer
2k views

Is my proof for a context free language correct? Same number of a's as b's

I have the following grammar G: $$ \begin{align*} &S \to aB|bA \\ &A \to a|aS|bAA \\ &B \to b|bS|aBB \end{align*} $$ I am going to prove that this language L(G) consists of words with the ...
4
votes
3answers
278 views

Designing a CFG that produces as many c's as the difference of numbers of a's and b's

The question is to design a CFG for the language of words that have as many c's as the difference of numbers of a's and b's, that is $\qquad\displaystyle L = \{(a^l)(b^m)(c^n) \mid l, m \in \mathbb{N}...
0
votes
0answers
62 views

How i can use Mathematical induction to prove CFG production? [duplicate]

If I have production $G_n$ $S \rightarrow A_i b_i \quad$ for $1 \le i \le n$ $A_i \rightarrow a_j A_i \mid a_j\quad$ for $1 \le i$ and $i \ne j$ Prove $G_n$ is sub-productions from $2n^2 - n$ ...
29
votes
4answers
24k views

How to prove that a grammar is unambiguous?

My problem is how can I prove that a grammar is unambiguous? I have the following grammar: $$S → statement ∣ \mbox{if } expression \mbox{ then } S ∣ \mbox{if } expression \mbox{ then } S \mbox{ else } ...

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