# Questions tagged [context-free]

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### Why is the Pumping Lemma sometimes called Bar-Hillel's Lemma?

There are several papers in the literature that refer to the Pumping Lemma for context free languages as Bar-Hillel's Lemma (for example, here, here, and on the Wikipedia page). However, the first ...
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### Deciding whether DCFG is visibly pushdown

Is the following problem decidable? If so, what's the best algorithm known? Instance: a deterministic pushdown automaton $A$ Question: Does there exist (i) some partition of the alphabet into push, ...
633 views

### Does PEG contain CFG?

Despite their considerable expressive power, all PEGs can be parsed in linear time using a tabular or memoizing parser (8). These properties strongly suggest that CFGs and PEGs define incomparable ...
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### Language of stack configurations of a pushdown automaton

Consider a pushdown automaton $A$ with stack alphabet $\Gamma$. Let $L$ be the language on $\Gamma$ of the stack configurations encountered during accepting runs of $A$. Is $L$ a context-free language?...
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### “Context” understanding in tree grammars

The Context-Free tree grammar has rules of the form: $A\rightarrow t$ or $A(x_1,\dots,x_n)\rightarrow t_x$, where $A\in N$, $t\in T(N\cup T)$, $t_x\in T(N\cup T\cup \{x_1,\dots,x_n\})$, $T(Z)$ ...
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### Variant of a proof using Ogden's lemma

I am trying to understand better the proof that the language $K=\{a^{i}b^{j}c^{k} ~|~ i \neq j, i \neq k, j \neq k$} is not context-free. (see It only looks like a homework problem…), and the use of ...
541 views

### Minimal context-free Grammar for a special one-letter Language

For natural numbers $n \geq 5$, $m \geq 2^{n-2} + 1$ the following context-free language is given: $$L_{n,m} = \{ a^i | 2 \leq i \leq m \} \setminus \{a^{2^i}|2 \leq i \leq n-2\}$$ Find and ...
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### Is it known if $CFL \subseteq NSPACE(o(log^2(n)))$?

$CFL$ is the class of context-free languages. Question Is $CFL$ known to be solvable in $o(log^{2}(n))$ non-deterministic space? What about $DCFL$?
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### Deciding whether an arbitrary context-free grammar generates a deterministic push-down automata?

I know that it's undecidable whether an arbitrary context-free grammar is ambiguous, but is it decidable whether that grammar is deterministic? I can't find the answer to this question anywhere on the ...
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### Context-Sensitive Grammar characteristic properties

This question can look like some kind of puzzle, but it is actually part of more complex applied problem. Let's consider subspace of Context-Sensitive Grammars, which contains grammars which can not ...
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### Necessary and sufficient condition for an infinite tree to be context-free

A Buchi automaton is non-empty iff it accepts an infinite word of the form $uv^\omega$ (here $u,v$ are finite words). In other words, if $\{w\}$ is an $\omega$-regular language, then it is of that ...
52 views

### A Context-Sensitive Grammar which cannot be recognised by a Parsing Expression Grammar

It is (currently) an open question of whether every context-free grammar can be recognised by some parsing expression grammar.  However, has it been proven that there exists an example of a ...
105 views

### Is scalable hardware support for LogCFL (= sAC^1) possible?

The (uniform) circuit classes $TC^0$, $NC^1$ and $sAC^1$ seem to lend themselves to efficient hardware implementation. But using an FPGA approach to create the circuits on the fly seems problematic, ...
635 views

### Decidability of CFG ambiguity

I have been trying to show the following language is undecidable. $L = \{ (\langle G \rangle , n ): G$ is a context-free grammar with an ambiguous string of length $\le n \}$. I think it is ...
264 views

### Non-uniform CFG ambiguity decidability

The uniform version (the version which we normally see) of deciding whether a CFG (Context Free Grammar) is ambiguous is undecidable. But here I'd like to know something about the non-uniform version ...