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Anya is live and ready to show you everything. Watch her strip, dance, and perform exclusive shows just for you. Interact in real-time and make your fantasies come true.
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hey, do you think Rick is on the side of P = NP?
yes, no, a bit of both, explain your answers?
I found a book specifically for finite model theory that contains like 80% of all the things that interest me in math... Let's just say my motivation is back.
(Semi-regularly updated) list of resources for (not only) young mathematicians interested in logic and all things related:
Igor Oliveira's survey article on the main results from complexity theory and bounded arithmetic is a good starting point if you're interested in these topics.
The Complexity Zoo for information on complexity classes. (For pdf version click here.)
The Proof Complexity Zoo for information on proof systems and relationships between them.
Computational Complexity blog for opinions and interesting blog posts about computational complexity and bunch of other stuff.
Very weak theories of arithmetic are absolutely fascinating to me. It seems like to prove anything nontrivial (or at least to prove bunch of nontrivial stuff in the same theory) you need to be able to reason about polynomial time functions.
For example the nice inclusions for Buss's hierarchy S^i_2 \subseteq T^i_2 \subseteq S^{i+1}_2 does not hold for T^0_2 and S^0_2 which are incomparable. Polynomial induction and length induction which are equivalent in all other theories above S^1_2 are not the same here. But if we add the MSP symbol to the language, suddenly we get much stronger reasoning. For example T^0_2(MSP) is equivalent to PV_1.
The funny thing is even separations of those weak theories are nontrivial. But it is the only place when we have actual unconditional separations! Basically the idea is to show that such weak reasoning power cannot prove some basic arithmtical statement - such as that every nontrivial devisor of 2 is even in the case of T^0_2 (funnily, this statement can be proven in S^0_2 lol)!
Anya is live and ready to show you everything. Watch her strip, dance, and perform exclusive shows just for you. Interact in real-time and make your fantasies come true.
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Is there something more erotic than live-texting your reading of a complexity paper by your crush to said crush.
No. I don't care that you improved the time of the algorithm from O(n^3) to O(n^2.8). It's polynomial. Chill.
But we already have a proof? Why do we need another proof?
You fool. We need as many proofs of a theorem as we can get. Oh we already have a proof in ZFC! Oh we already have a proof in PA! That's nice but sometimes you want to prove that shit in $S^1_2$! And the original proof cannot be formalized there! Provability of results in weaker theories of arithmetic tells us important things about what is feasibly computable, we should care about that stuff.
