2025 on Tumblr: Trends That Defined the Year
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izzy's playlists!
I'd rather be in outer space 🛸
Jules of Nature
"I'm Dorothy Gale from Kansas"

❣ Chile in a Photography ❣
Cosimo Galluzzi
Sweet Seals For You, Always
Mike Driver

pixel skylines

祝日 / Permanent Vacation
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Not today Justin
Claire Keane
h

titsay

Origami Around
Sade Olutola
hello vonnie

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@siliconaddict
By Avogado6
My very first tiger drawing and my latest
when the characters never really make peace with it
Moebius, Le fil d'Ariane
家主おきるです
オレのたんぶらも おきるです
Hey, get up landlady, and get my tumblr up
It's crazy, just how far we're from proving P ≠ NP. It is known that LOGSPACE ⊆ NLOGSPACE ⊆ P ⊆ NP, but so far we haven't even managed to rule out LOGSPACE = NP, even though the former is something logarithmic and the latter is (by current knowledge) something exponential.
By the way, in the above inclusions only NLOGSPACE ⊆ P is nontrivial but easy to prove: Any NLOGSPACE Turing machine (NL-TM) that has S states and uses ≤ k × log n memory has S × 2^(k × log n) = S × nᵏ many configurations. A P-TM can list all those configurations and simulate the NL-TM's computation paths by running, say, breadth-first search on the start configuration. The P-TM then accepts iff it reaches any of the NL-TM's accepting configurations. Since breadth-first search takes O((S × nᵏ)²) = O(n²ᵏ) time, any NLOGSPACE problem can indeed be solved in polynomial time.
idiot at wizard school just said "i have devised the perfect mana nullification field rendering me impervious to all forms of magic!" i figure he should've taken a few more interdisciplinary courses because i tweaked the timing on a gravitation spell to throw a giant boulder at him. the moment I released the spell it stopped being a sorcery equation and started being a physics one
no rest for me and im not even that wicked ?