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user:1234 user:me (yours) |
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score:3 (3+) score:0 (none) |
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answers:3 (3+) answers:0 (none) isaccepted:yes hasaccepted:no inquestion:1234 |
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title:apples body:"apples oranges" |
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Results tagged with closure-properties
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user 21755
Questions about operations on objects of some kind that result in objects of the same kind.
8
votes
1
answer
1k
views
If L is context-free, must FH(L) be context-free?
Define $FH(L) = \{x \in \Sigma^* : \exists y \in \Sigma^* \text{ with } |x| = |y| \text{ such that } xy \in L\}$. In other words, $FH(L)$ is the set of first halves of even length strings in $L$. …
- 493
2
votes
2
answers
136
views
Prove that REG is closed against removing all but lexicographicaly largest words (per length)
Let $\Sigma_n = \{0, 1, ... , n-1\}$. Suppose $L \subseteq$ $\Sigma^*_n$, and let
$\qquad\displaystyle\mathcal{B}(L) = \{ x \in L : x = \textrm{lex}\max L_m, m \in \mathbb{N}_0 \}$,
where $L_m = L \ …
- 493
4
votes
1
answer
861
views
Given a non-deterministic Mealy machine $M$, if $L$ is regular, is $M(L)$ regular?
Consider a nondeterministic Mealy machine, $M$, defined as follows:
$M = (Q, \Sigma, \Delta, \delta, \tau, q_0)$ where
$Q$ is a finite set of states
$\Sigma$ is an input alphabet
$\Delta$ is an outp …
- 493
0
votes
1
answer
141
views
For two regular languages, why is the set of words from one that don't have a subsequence in...
In general, a string $x$ is a subsequence of $w = w_1\dots w_n$ if there are integers $i_1<\dots< i_k$ such that $x = w_{i_1}\dots w_{i_k}$. The subsequence is proper if $k < n$ and $k > 0$.
With th …
- 493