Skip to main content
Search type Search syntax
Tags [tag]
Exact "words here"
Author user:1234
user:me (yours)
Score score:3 (3+)
score:0 (none)
Answers answers:3 (3+)
answers:0 (none)
isaccepted:yes
hasaccepted:no
inquestion:1234
Views views:250
Code code:"if (foo != bar)"
Sections title:apples
body:"apples oranges"
URL url:"*.example.com"
Saves in:saves
Status closed:yes
duplicate:no
migrated:no
wiki:no
Types is:question
is:answer
Exclude -[tag]
-apples
For more details on advanced search visit our help page
Results tagged with
Search options not deleted user 20340

P versus NP and other resource-bounded computation.

5 votes
1 answer
263 views

Is there a fine grained relation between LH and AC0?

The wikipedia article states that the Logarithmic time hierarchy (LH) is equal to FO-uniform AC0. But since the natural way to think about LH is in terms of its levels (with DLogTime at the zeroth lev …
Thomas Klimpel's user avatar
2 votes
Accepted

Relativized world where $L^A=NP^A$

My question is just whether there is a known relativization barrier. Yes, there is a known relativization barrier. It's given by $A:=TQBF$, because Emil Jeřábek (see comments) is right: the state …
9 votes
Accepted

Is the finite inverse semigroup isomorphism problem GI-complete?

Yes, the finite inverse semigroup isomorphism problem is GI-complete! This is a corollary of Theorem: Lattice isomorphism is isomorphism complete from section 7.2 Lattices and Posets in Boot …
Thomas Klimpel's user avatar
4 votes
0 answers
193 views

Can coNLogTime verification be used instead of PTime verification when characterising NP?

I recently read a paper that presented a proof calculus where the verification of whether a given proof is valid was NL-complete. The authors apparently decided that the checking procedure was not loc …
Thomas Klimpel's user avatar
2 votes
0 answers
114 views

Is equivalence of uniform AC0 decidable?

Is there a representation of the functions from $\mathsf{DLogTime}$-uniform $\mathsf{AC}^0$ for which equivalence is decidable? Since the languages defined by nondeterministic pushdown automata belon …
Thomas Klimpel's user avatar
0 votes
0 answers
102 views

Useful primitives CPUs could provide, from TC0 (or NC1)

I just listened to XYZ talking about "How Universal Is the Idea of Numbers?", and bashing the concept as an accidental historical artifact. He suggested that totally different computational primitives …
Thomas Klimpel's user avatar
11 votes
1 answer
317 views

Is the finite inverse semigroup isomorphism problem GI-complete?

Is the finite inverse semigroup isomorphism problem GI-complete? Here the finite inverse semigroups are assumed to be given by their multiplication tables.
Thomas Klimpel's user avatar
5 votes
1 answer
383 views

Relativized world where $L^A=NP^A$

I wonder1 whether there is a known relativization barrier against proving $L\neq NP$. Hence I'm looking for a language $A$ for which $L^A=NP^A$. My first idea was to try $A:=SAT$, but then I thought …
Thomas Klimpel's user avatar
13 votes
1 answer
255 views

Conclusions from reverse mathematical strength of graph minor theorem

Say we have a graph property which can be checked in nondeterministic polynomial time, and a proof in a weak formal system (say RCA0) that the property is minor closed. Can we say anything about the s …
Thomas Klimpel's user avatar
16 votes
Accepted

What evidence is there that Graph Isomorphism is not in $P$?

Before this question, my opinion was that Graph Isomorphism might be in P, i.e. that there is no evidence to believe that GI is not in P. So I asked myself what would count as evidence for me: If ther …
Thomas Klimpel's user avatar
0 votes

Limits to Parallel Computing

I answered the similar question Are there any famous problems/algorithms in scientific computing that cannot be sped up by parallelisation on the Computational Science site. Let me quote it here, beca …
0 votes

Reasons to believe $P \ne NP \cap coNP$ (or not)

I believe that there exists very space efficient high quality random number generators. Despite this belief, I normally use Mersenne twister in my code, which is high quality, but not very space effic …
Thomas Klimpel's user avatar
5 votes

Reasons to believe $P \ne NP \cap coNP$ (or not)

Theorem 3.1 of One-Way Permutations and Self-Witnessing Languages C. Homan and M. Thakur, Journal of Computer and System Sciences, 67(3):608-622, November 2003. [ as .pdf ] states that $P≠UP∩coUP$ if …
3 votes

The unreasonable power of non-uniformity

I have the impression that the real issue here is the unreasonable heavy burden of proof, not the unreasonable power of non-uniformity. As the answers by chazisop and András Salamon already stress, un …
Thomas Klimpel's user avatar
2 votes

Is there a theory that combines category theory/abstract algebra and computational complexity?

This answer about isomorphisms between formal languages combines algebraic results from the theory of codes with notions from category theory to investigate possible notions of equivalence and isomorp …

15 30 50 per page