Questions tagged [closure-properties]

Questions about operations on objects of some kind that result in objects of the same kind.

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9
votes
3answers
2k views

If $L$ is context-free and $R$ is regular, then $L / R$ is context-free?

I'm am stuck solving the next exercise: Argue that if $L$ is context-free and $R$ is regular, then $L / R = \{ w \mid \exists x \in R \;\text{s.t}\; wx \in L\} $ (i.e. the right quotient) is context-...
5
votes
1answer
356 views

The operator $A(L)= \{w \mid ww \in L\}$

Consider the operator $A(L)= \{w \mid ww \in L\}$. Apparently, the class of context free languages is not closed against $A$. Still, after a lot of thinking, I can't find any CFL for which $A(L)$ ...
13
votes
2answers
1k views

Closure against right quotient with a fixed language

I'd really love your help with the following: For any fixed $L_2$ I need to decide whether there is closure under the following operators: $A_r(L)=\{x \mid \exists y \in L_2 : xy \in L\}$ $A_l(L)=\{...
5
votes
1answer
288 views

Closure against the operator $A(L)=\{ww^Rw \mid w \in L \wedge |w| \lt 2007\}$

I would like your help with the following question: Let $L$ be a language, and operator $A(L)=\{\,ww^Rw \mid w \in L\ \wedge\ |w| \lt 2007\,\}$ where $x^R$ is the reversed string of $x$. Which of ...
11
votes
1answer
3k views

Is an infinite union of context-free languages always context-free?

Let $L_1$, $L_2$, $L_3$, $\dots$ be an infinite sequence of context-free languages, each of which is defined over a common alphabet $Σ$. Let $L$ be the infinite union of $L_1$, $L_2$, $L_3$, $\dots $; i....
8
votes
1answer
566 views

Proving closure under complementation of languages accepted by min-heap automata

This is a follow-up question of this one. In a previous question about exotic state machines, Alex ten Brink and Raphael addressed the computational capabilities of a peculiar kind of state machine: ...