Linked Questions

2
votes
3answers
2k views

Is this language LL(1) parseable?

I tried to find a simple example for a language that is not parseable with an LL(1) parser. I finally found this language. $$L=\{a^nb^m|n,m\in\mathbb N\land n\ge m\}$$ Is my hypothesis true or is ...
5
votes
2answers
806 views

Pumping lemma: if you can keep pumping, what does this tell you?

Hypothetically, let's say you are using the pumping lemma for either regular or context free languages. Now using either, you come across a case that remains true despite pumping it. In this situation,...
4
votes
2answers
2k views

Can a two-stack PDA accept language $a^nb^mc^nd^m$ which is not context-free?

Can a two-stack PDA accept language $L=\{a^nb^mc^nd^m \mid n \geq m\}$, which has no context-free grammar? I don't believe this has a context-free grammar, but please correct me if I'm wrong.
1
vote
1answer
4k views

How to prove {a^(n^2) | n>0} is not context-free?

So I have a language: $$ L = \{a^{n^2} \mid n > 0\} $$ I need to prove that this language isn't context-free using the pumping lemma. I have a vague thought process as to how to do the proof but I'...
3
votes
3answers
861 views

Structure of a Pumping Lemma proof: contradiction or counterexample?

This site is full of Pumping Lemma questions, and I do admit I've not read them all. I've tried some proofs myself and they seem to work, but I can't find anywhere what is the (general) exact ...
3
votes
1answer
2k views

Are permutations of context-free languages context-free?

Given a context-free language $L$, define the language $p(L)$ as containing all permutations of strings in $L$ (i.e. all strings in $L$ such that the order of symbols is not important). Is $p(L)$ ...
3
votes
2answers
2k views

Is Python a context-free language?

From Wikipedia: Off-side_rule#Implementation, there is a statement: ...This requires that the lexer hold state, namely the current indentation level, and thus can detect changes in indentation ...
2
votes
1answer
2k views

Use pumping lemma to show L is not context free

Show that L = $\{0^{2^n}| n\geq 0\}$ is not a context free language. Let string $s = 0^{2^p}$. Then we know we can write $s$ as $s = uvxyz$. I know that |vy| > 0 and $|vxy| \leq p$. So how do I ...
1
vote
2answers
2k views

Proof that a language involving $gcd$ is not context-free

How would you prove that the following language is not context-free? $$ L= \{a^n b^m |\, gcd(n,m)=1 \}$$ I suspect the solution uses the pumping lemma, but I'm not sure how to apply it.
8
votes
1answer
449 views

Is this language Context-Free?

Is the language $$L = \{a,b\}^* \setminus \{(a^nb^n)^n\mid n \geq1 \}$$ context-free? I believe that the answer is that it is not a CFL, but I can't prove it by Ogden's lemma or Pumping lemma.
2
votes
2answers
990 views

Show that $0^i$ where $i$ is a power of 2 is not context free

I'm having difficulty trying to use the pumping lemma in order to show that $L= \{0^i \mid \ i \text{ is a power of 2 }\} $ is not context free. I"m starting by stating that $ s = 0^p$ and then $ s = ...
0
votes
1answer
1k views

PDA or CFG for language $L= \{a^ib^j | 2i \leq 2j \leq 3i, i>0\}$

Can someone help with this $L= \{a^ib^j | 2i \leq 2j \leq 3i, i>0\}$
16
votes
3answers
987 views

Algorithm to test whether a language is context-free

Is there an algorithm/systematic procedure to test whether a language is context-free? In other words, given a language specified in algebraic form (think of something like $L=\{a^n b^n a^n : n \in \...
1
vote
1answer
2k views

Prove that {0^{n^3} | n≥0} is not context free

I'm not very comfortable with pumping lemma for context-free grammar. I understand the sufficient conditions that must hold but proving it gets me everytime. For example, I need to prove whether $L = \...
6
votes
1answer
271 views

Why do we study closure properties of formal languages?

In automata theory we study formal languages like Regular, CF, CS and etc. and each of them have their own closure properties under union, intersection, star and etc. . I like to know, why it is ...

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