# Tag Info

Accepted

### Number of words of length n in a context-free language

Every context-free language has either polynomial growth or exponential growth. In the notation of the question poser: Either there is a polynomial $p$ so that $w_n\le p(n)$ for all $n$ Or there ...
Accepted

### Are DPDAs without a $\epsilon$ moves as powerful as DPDAs with them?

Perhaps I found some relevant information in: Jean-Michel Autebert, Jean Berstel, Luc Boasson; Context-Free Languages and Pushdown Automata; Handbook of Formal Languages; 1997, pp 111-174 DPDAs ...

### Languages that we cannot (dis)prove to be Context-Free

Another good one is the complement of the set $S$ of contiguous subwords (aka "factors") of the Thue-Morse sequence ${\bf t} = 0110100110010110 \cdots$. To give some context, Jean Berstel proved ...

### Languages that we cannot (dis)prove to be Context-Free

How about the language $L_{TP}$ of twin primes? I.e., all pairs of natural numbers $(p,p')$ (represented, say, in unary), such that $p,p'$ are both prime and $p'=p+2$? If twin primes conjecture is ...
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### Size of complement of context-free language

From the proof that determining if a CFL ${L}$ = $\Sigma^*$ is undecidable, the set of strings $ID_0\#ID_1^R\#ID_2\#ID_3^R\#\ldots\#ID_t$ where $ID_0,ID_1,\ldots,ID_t$ is a list of the configurations ...
Accepted

### Is the complement of { www | … } context-free?

Still CFL I believe, with an adaptation of the classical proof. Here's a sketch. Consider $L = \{xyz : |x|=|y|=|z| \land (x \neq y \lor y \neq z)\}$, which is the complement of $\{www\}$, with the ...
Accepted

### What is the state complexity of the copy language?

The technique described by Yuval: Do there exists polynomial size CFG that describe this finite language? ( you may also read: Lower bounds on the size of CFGs for specific finite languages ) ...
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### Known and described subclasses of Context-Free Grammars class

Density might be interesting concept for you. The density function is defined as $$\delta_L(n) := |L\cap \Sigma^n|,$$ where $\Sigma^n$ denotes the set of all strings of length $n$ over $\Sigma$. ...
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### Is equivalence of unambiguous context-free languages decidable?

This is currently an open problem. As correctly pointed out, if it is decidable, then one expects the proof to be hard since it generalises the famous DPDA equivalence problem. On the other hand, the ...

### Is the complement of { www | … } context-free?

Here is the way I think about solving this problem, with a PDA. In my opinion, it's intuitively clearer. A word $x$ is not of the form $www$ iff either (i) $|x| \not\equiv 0$ (mod 3), which is easy ...
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### A reference for a "more algebraic" approach to pushdown automata and CFLs?

Sakarovitch's PhD thesis from 1976, titled Monoïdes syntactiques et languages algébriques (syntactic monoids and algebraic languages), revolves around this topic. At the time, this led to the ...

### How is proving a context free language to be ambiguous undecidable?

The answer by apolge presents the proof that it is undecidable whether an arbitrary context free grammar is ambiguous. The question of whether a context free language is inherently ambiguous is a ...

### Maximum shortest word accepted by pushdown automata

The precise answer depends on your model of PDA (models differ among different authors; compare Sipser to Hopcroft &Ullman). And number of states alone is not a good measure for PDA's, because ...

### Does there exist a hardest DCFL?

The paper J.-M. Autebert, Une note sur le cylindre des langages déterministes, Theoretical Computer Science 8 (1979), 395-399 gives a short proof of the following result (credited to Greibach) ...

### Does there exist a hardest DCFL?

There actually is a hardest DCFL, which is a deterministic version of Greibach's; it was introduced by Sudborough in 78 in On deterministic context-free languages, multihead automata, and the ...

### Does there exist a hardest DCFL?

An identical homomorphism characterization of DCFL does not seem to be possible. The following is extracted from Greibach's original paper. We show that every context-free language can be expressed ...