Questions tagged [context-free]

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

166 questions
60k views

How to prove that a language is not context-free?

We learned about the class of context-free languages $\mathrm{CFL}$. It is characterised by both context-free grammars and pushdown automata so it is easy to show that a given language is context-free....
23k 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 ...
11k views

Show that { xy ∣ |x| = |y|, x ≠ y } is context-free

I remember coming across the following question about a language that supposedly is context-free, but I was unable to find a proof of the fact. Have I perhaps misremembered the question? Anyway, here'...
19k views

8k views

Two-State Turing Machine for Parenthesis Matching

In college we have been learning about theory of computation in general and Turing machines more specifically. One of the great theoretical results is that at the cost of a potentially large alphabet (...
21k views

Convert CFG to PDA

Is there any set of rules or methods to convert any context free grammar to a push down automata? I already found some slides online but I wasn't able to understand them. In slide 10 he speaks ...
298 views

What's the reason for the second condition of the pumping lemma(s)?

For a language $L$ with pumping length $p$, and a string $s\in L$, the pumping lemmas are as follows: Regular version: If $|s| \geq p$, then $s$ can be written as $xyz$, satisfying the following ...
3k views

complexity of determining whether a language given by context free grammar is empty

I know that it is decidable problem to check whether given context free grammar represents empty language -- for instance, AFAIR one could convert it to Chomsky normal form, and then check if any word ...
Let $G$ be a context-free grammar. A string of terminals and nonterminals of $G$ is said to be a sentential form of $G$ if you can obtain it by applying productions of $G$ zero or more times to the ...