Tagging - 2021-01-06

Martin Sleziak

6:28 AM

@MartinSleziak deleted-tag The tag topology is gone.

Martin Sleziak

1:31 PM

new-tag A new tag pushdown-automata was created.

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Q: Is pushdown transduction of a periodic sequence periodic?

Let’s define a pushdown transducer as a 9-tuple $V = (A, B, S, Q_A, Q_S, \phi, \psi, \chi, q_0)$, where $A$ is the finite input alphabet, $B$ is the finite output alphabet, $S$ is the finite stack alphabet, $Q_A$ are the finite set of read-from-input states, $Q_S$ is the finite set of read-from-s...

4

Q: Is the set of pushdown transductions closed under composition?

Let’s define a pushdown transducer as a 9-tuple $V = (A, B, S, Q_A, Q_S, \phi, \psi, \chi, q_0)$, where $A$ is the finite input alphabet, $B$ is the finite output alphabet, $S$ is the finite stack alphabet, $Q_A$ are the finite set of read-from-input states, $Q_S$ is the finite set of read-from-s...

abstract-algebra discrete-mathematics automata semigroups pushdown-automata

1

Q: Does both the language and its complement being context free imply it being deterministic context-free?

Suppose $L \subset A^*$ is context free and $A^*\setminus L$ is also context free. Does it mean, that $L$ is deterministic context free? If it is not, I would like to see a counterexample (I failed to construct one myself). Note that the converse is true. Moreover, a complement to a determinist...

discrete-mathematics formal-languages automata context-free-grammar pushdown-automata

Martin Sleziak

2:58 PM

1

A: Tag management 2021

$\textbf{Proposal}:\;$ Create the tag Dot-product There is a tag for cross-product, but not one for dot-product. There is a tag for inner-product-space, but that is more abstract than the usual dot product for $\mathbb R^n$.

Seems like a synonym would be the ideal solution here, redirecting dot-product to inner-product-space But on the other hand this may confuse users who would be the target audience of dot-product — Alexander Gruber ♦ yesterday

@AlexanderGruber I agree that a dot-product -> inner-product-space synonym would be ideal. I have edited the inner product space tag wiki in anticipation of such a move (i.e. I have highlighted the dot product a bit more). The goal of the edits was to prevent confusion on the part of "dot product" users. — Xander Henderson ♦ yesterday

Tag-excerpt: math.stackexchange.com/posts/49900/revisions Tag-wiki: math.stackexchange.com/posts/49899/revisions

The current revision of the tag-excerpt:

> For questions about inner products and inner product spaces, including questions about the dot product. An inner product space is a vector space equipped with an inner product. The dot product (seen in multivariable calculus and linear algebra) is a simple example of an inner product—other inner products may be seen as generalizations of the dot product.

@XanderHenderson For me, the — is displayed — as and not as —. So maybe it should be replaced by the — character.

Or is it supposed to work in the tag-excerpt?

Xander Henderson

@MartinSleziak It renders correctly on my end. :\

Martin Sleziak

That's interesting.

Xander Henderson

But maybe there is some interaction with ChatJax and the various other scripts I have running which makes it look correct.

I'll change it (if it fails somewhere, it is likely it fails in other places, too).

Martin Sleziak

I was about to say that it renders for me correctly in the pop-up and not in the tag-info. But most likely it was because you manage to edit it before I took the second screenshot.

Xander Henderson

Heh. :P

Martin Sleziak

3:08 PM

@quid Since I know that you and me are on the opposite sides of the spectrum concerning tag-synonyms and that you opposed some tag synonyms that looked fine to me, I wanted to let you know that the synonym dot-product $\to$ inner-product-space is being discussed.

See the post linked above and the comments under that post.

Martin Sleziak

5:39 PM

@MartinSleziak tag-wikis The tag pushdown-automata now has a tag-excerpt: math.stackexchange.com/posts/3975054/revisions math.stackexchange.com/review/suggested-edits/1519666

Pushdown automaton

In the theory of computation, a branch of theoretical computer science, a pushdown automaton (PDA) is a type of automaton that employs a stack. Pushdown automata are used in theories about what can be computed by machines. They are more capable than finite-state machines but less capable than Turing machines. Deterministic pushdown automata can recognize all deterministic context-free languages while nondeterministic ones can recognize all context-free languages, with the former often used in parser design. The term "pushdown" refers to the fact that the stack can be regarded as being "pushed...

quid

8:49 PM

@MartinSleziak I guess I can live with that one. Though I don't get why the other one needs the "spaces"

I mean "inner-product" or "inner-products" would be just as good.

2

Xander Henderson

I like "inner-products".

Martin Sleziak

Perhaps the suggestion to rename this to inner-product or inner-products could be also mentioned in the comments.

It sounds reasonable, if we want this as a common tag for the more abstract concept and for the usual inner product in $\mathbb R^n$.

Xander Henderson

@MartinSleziak I think that I will post a new answer to the tag management thread which puts forward a concrete proposal for creating and synonymizing tags.

J. W. Tanner's answer seems like the wrong venue.

Martin Sleziak

A separate answer would certainly mean more visibility for that suggestion.

Feeds

9:32 PM

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A: Tag management 2021

Proposal: Rename the inner-product-spaces to inner-products. Create the tag synonym inner-product-spaces $\to$ inner-products. Create the tag synonym dot-product $\to$ inner-products. Create the tag synonym scalar-product $\to$ inner-products. This is related to, but distinct from, J. W. Tanner...

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$Mathematics$ Tagging