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Results tagged with computational-complexity
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user 7092
This is a branch that includes: computational complexity theory; complexity classes, NP-completeness and other completeness concepts; oracle analogues of complexity classes; complexity-theoretic computational models; regular languages; context-free languages; Komolgorov Complexity and so on.
10
votes
Undecidable infinite analogs of NP-complete problems?
There's at least one notable counter-example: solving the mate-in-$poly(n)$ problem for chess on an $n\times n$ board is PSPACE-complete and thus NP-hard (per https://arxiv.org/abs/2010.09271 ), but t …
4
votes
Counting $\mathrm{mod}\:p$ solutions of Diophantine equation in two variables taking $O(p^2)...
At least for fixed degree, the answer appears to be 'no' — it seems to be well-established that the number of roots of a univariate polynomial $g(x)$ of degree $d$ modulo a prime $p$ can be determined …
- 1,951
3
votes
1
answer
1k
views
Is there a promise version of 3-coloring equivalent to Graph Isomorphism?
The discussion at Decision problem restricted to inputs that satisfy some necessary condition. got me thinking about specific promises on a graph that would reduce the complexity of the coloring probl …
- 1,951
1
vote
Completeness, easiest, hardest problems
It sounds like what you're talking about is the very basics of recursion theory, particularly the Turing degrees and even more specifically the degree 0' that contains the complete set K (defined as t …
- 1,951
1
vote
Indexing schemes of binary sequences
You want Volume 4, Fascicle 3 of Knuth's The Art of Computer Programming, chapter 7.2.1.3: "Generating All Combinations" - I won't include links because everyone has a favorite online bookseller, but …
- 1,951