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# 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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### CFG where u has same number of 1s as v [closed]

$$L=\{uv\in\{0,1,2\}^*\mid u\in\{0,1\}^*,v\in\{1,2\}^*, \text{ and }u\text{ has the same number of 1s as }v\}.$$ Here is my attempt solution, but it is not completely correct, any hint is appreciated ...
75 views

### Is there a context-free grammar for $L = \{a^{2^n}| n \geq 1\}$? [duplicate]

I was trying to find a cf-grammar for $L = \{a^{2^n}| n \geq 1\}$ but I cannot seem to find one. Is there a cf-grammar or does it not exist because of the quadratic-exponent?
633 views

### Decidability of determining whether a context-free grammar generates all strings in 1*

How could I prove that the following language is decidable? $\{\langle G\rangle \mid G\ \text{is a CFG over}\ \{0,1\}\ \text{and}\ 1^* \subseteq L(G)\}$ P.S. It's the problem 4.15 of the third ...
52 views

### Context-free grammars for two languages

How do I write context-free grammars for the following languages? $B_2 = \{0^n1^n \mid n > 0\} \cup \{0^n1^{2n} \mid n > 0\}$ $B_3 = \{a^nb^mc^k \mid k = n+m\}$ Can someone help me? I'm not ...