58
votes
9answers
6k views

Analogues of P vs. NP in the history of mathematics

Recently I wrote a blog post entitled "The Scientific Case for P≠NP". The argument I tried to articulate there is that there seems to be an "invisible electric fence" separating the problems in P ...
3
votes
1answer
178 views

Class Separation, Oracles, Relativization

It is known, there exists oracles A, B s.t.: $P^A = NP^A; P^B \neq NP^B$, showing that any proof of P vs NP must be non-relativizing. Questions: (1) Can we actually use Oracles to separate ...
3
votes
1answer
257 views

Interesting complexity classes $PR \subsetneq c \subsetneq R$

I'm working on a proof-checker that can verify termination proofs. The fundamental method it provides for constructing such proofs is to translate the program into primitive recursion. Basically, I ...
11
votes
7answers
2k views

Most 'obvious' open problems in complexity theory

What open problems in computational complexity theory have the most 'obvious' answers, regardless of whether that answer is true or false? The problems I'm talking about certainly have more 'obvious' ...
5
votes
3answers
1k views

When would you read a paper claiming to have settled a long open problem like $P$ vs. $NP$? [closed]

From time to time, people announce papers claiming to have settled long open problems like $P$ vs. $NP$. There have been many attempts, reading them is time-consuming, and finding bugs in their ...
2
votes
1answer
652 views

Probability of system failure in a distributed network

I am trying to build a mathematical model of the availability of a file in a distributed file-system. The system works like this: a node $x$ stores a file $f$ (encoed using erasure codes) at $rb$ ...
4
votes
5answers
681 views

Quantum Computing Complexity?

After reading a recent post on Church's Thesis, I ran into Turing-Church's Strong Thesis, that may be potentially disproven by advances in Quantum Computing. Does anyone know of a good resource that ...