Linked Questions

25
votes
4answers
1k views

What specific evidence is there for P = RP?

RP is the class of problems decidable by a nondeterministic Turing machine that terminates in polynomial time, but that is also allowed one-sided error. P is the usual class of problems decidable by ...
24
votes
4answers
8k views

Major unsolved problems in distributed systems?

Inspired by this question, what are the major problems and existing solutions which needs improvement in (theoretical) distributed systems domain. Something like membership protocols, data ...
34
votes
3answers
3k views

Consequences of Factoring being in P?

Factoring is not known to be NP-complete. This question asked for consequences of Factoring being NP-complete. Curiously, no one asked for consequences of Factoring being in P (maybe because such a ...
11
votes
3answers
6k views

What does research in theoretical computer science involve?

I am trying to understand what is involved in theoretical computer science research. What do theoretical computer scientists do? I know a significant time is spent on teaching, supervising graduate ...
7
votes
3answers
5k views

Polynomial Time Algorithm for Graph Isomorphism Testing [closed]

"Michael I. Trofimov" claims that he has found a poly-time algorithm for graph isomorphism, which works for all graphs. The paper is given in arXiv. The companion website gives a proof-of-concept ...
39
votes
2answers
2k views

Are the problems PRIMES, FACTORING known to be P-hard?

Let PRIMES (a.k.a. primality testing) be the problem: Given a natural number $n$, is $n$ a prime number? Let FACTORING be the problem: Given natural numbers $n$, $m$ with $1 \leq m \leq n$, ...
25
votes
2answers
4k views

What are the consequences of factoring being NP-complete?

Are there any references covering this?
8
votes
2answers
565 views

Is there a list of known problems?

Is there a database of known problems with information about their complexity and algorithms, related problems, references etc that is available to us? [If not, can we make one? I know this is off ...
7
votes
2answers
894 views

Sources of open problems?

I'm wondering if there are some known sources of open TCS problems? I'm a junior studying math/CS and would like to know of some accessible problems that I could start thinking about! Thanks so much!...
21
votes
1answer
2k views

Is there a proof that addition is faster than multiplication?

The best upper bound known on the time complexity of multiplication is Martin Fürer's bound $n\log n2^{O(\log^* n)}$, which is more than linear time complexity of addition. Do we have a proof that ...
14
votes
1answer
700 views

Is Quasi-polynomial time in PSPACE?

I had done some search on this but I was not able to find an answer either way. Huck answered it fully. Thanks :)
2
votes
1answer
359 views

Complexity lower bound of finding the factorial of a number

I was wondering about the complexity of the factorial of a number mostly because this problem is not referenced in the complexity books I have read. Two similar problems, Matrix Multiplication and ...
-2
votes
1answer
156 views

Evidence integer multiplication is in linear time?

After millenia of quest we have identified two $n$ bit integers can be multiplied in $O(n\log n)$ time. Please refer details in https://www.quantamagazine.org/mathematicians-discover-the-perfect-way-...
-2
votes
1answer
261 views

Finding research problem for PhD(TCS)? [closed]

I am a theoratical computer science PhD student. I am wanted some suggestion in how to find research problem for PhD research. I have supervisor and he has given me first problem. We had get progress ...
3
votes
0answers
261 views

Why can't we have superlinear bounds on Boolean circuit size for an explicit function?

I am interested about the minimal size (number of gates) of a family of circuits (with negation) over a complete Boolean basis (with fanin 2) that computes some explicit Boolean function. (In other ...

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