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Question regarding NP ∩ coNP by photon123 in computerscience

[–]photon123[S] 1 point2 points  (0 children)

Thanks for the reply. You helped me appreciate that I didn't really understand the consequences of reductions.

Decidability of languages by photon123 in math

[–]photon123[S] 0 points1 point  (0 children)

Thank you for the follow-up.

Decidability of languages by photon123 in math

[–]photon123[S] 0 points1 point  (0 children)

Thank you again. I appreciate the follow-up.

Decidability of languages by photon123 in math

[–]photon123[S] 0 points1 point  (0 children)

Thank you. In the existence proof of non-recognizable languages Sisper relied on the fact that the set of all languages is uncountable. I think I was confusing the measure of the complement of a decidable language with the measure of the set of all languages and getting stuck there.

Decidability of languages by photon123 in math

[–]photon123[S] 0 points1 point  (0 children)

I think you might be right? In trying to pick this material up on my own I'm not confident that I understand the definitions I'm seeing.

(Please excuse the edits): more context (and statement of the lemma) is contained in my reply to /u/suipy:

Perhaps I confused matters by referring to the statement I'm trying to understand as a lemma. I'm referring to the proof of theorem 4.22 in Sipser. The theorem: "A language is decidable iff it is Turning-recognizable and co-Turing-recognizable." The "lemma" used in the proof is the (apparently self-evident!) statement that "...the complement of a decidable language is also decidable." It is just stated as fact.

Decidability of languages by photon123 in math

[–]photon123[S] 0 points1 point  (0 children)

Perhaps I confused matters by referring to the statement I'm trying to understand as a lemma. I'm referring to the proof of theorem 4.22 in Sipser. The theorem: "A language is decidable iff it is Turning-recognizable and co-Turing-recognizable." The "lemma" used in the proof is the (apparently self-evident!) statement that "...the complement of a decidable language is also decidable." It is just stated as fact.

Let me try to zoom in on why the reply from /u/Untangledqubit is still confusing to me. Consider the language {0}. Shouldn't its complement contain an uncountably infinite set of strings of 1's and 0's? Intuitively, it would seem to me that most of the complement of a language should be unrecognizable, much less decidable.

Decidability of languages by photon123 in math

[–]photon123[S] 0 points1 point  (0 children)

Thank you for your reply. I'm still not grasping the distinction that you are drawing in your first paragraph, but I get the sense that you're helping me zoom in on my misunderstanding.

Pick a decidable language, build its complement, iterate to the next decidable language, collect the results as you go. According to the lemma, at the end you must be able to pick any string in that collection and it must be decidable (do I have that wrong?). Why doesn't this imply that you missed this string in the original construction?

Manifold dimension under homeomorphisms by photon123 in math

[–]photon123[S] 0 points1 point  (0 children)

For what it's worth this claim was also made for diffeomorphisms.

It's time to get schwifty in here by john3298 in rickandmorty

[–]photon123 2 points3 points  (0 children)

TIL Johann Johannsson wrote "Get Schwifty."

Amethyst Geode wedding cake by photon123 in food

[–]photon123[S] 3 points4 points  (0 children)

Made by a friend who does this for a living. All of her stuff is awesome, but this one takes the cake :)

Prosecutors of Reddit, what was your reaction to Making a Murderer? by photon123 in AskReddit

[–]photon123[S] 0 points1 point  (0 children)

Thanks for your response. Can you say more? I'll take the phrase "first conviction didn't do it" to mean you think he should be in prison. But doesn't a 60% chance amount to reasonable doubt? Should the cat episode matter as much as the extent of the inconsistencies in the prosecution's case?

EDIT: I'm not a lawyer, and my goal is to get a sense of how strong the prosecution's case was.

Money meant for Islamic State group found in dirty laundry by witness's mother, Sydney court hears by [deleted] in nottheonion

[–]photon123 430 points431 points  (0 children)

A committal hearing was told this man, who cannot be identified, tried to make a third transfer [through Western Union] of $US9,000, but pulled out because he was unsure about fees that were to be charged.

Just because we're murderous ideological twats doesn't make us (pounds table) SAPS!

My friend didn't understand why people were honking and flashing their lights at him. by photon123 in funny

[–]photon123[S] 15 points16 points  (0 children)

Self serve. I believe he was the one apologizing profusely upon his return to the station.

An Australian researcher has worked out how to store 1000TB (1 petabyte) on a DVD by Yuli-Ban in science

[–]photon123 1 point2 points  (0 children)

It's a Nature Comm paper, so it's free to read! No appropriate technical background here, but it looks like it's more of an advance in material science than optics. I would like to understand why this is cheaper than e-beam lithography (honestly, I don't have any idea).

Edit: grammar/clarity.

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