Questions tagged [space-complexity]
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10
questions
14
votes
1answer
742 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 :)
19
votes
2answers
926 views
What is the space complexity of calculating Eigenvalues?
I am looking for a survey paper or a book covering results
about the space complexity of common linear algebra operations
such as matrix rank, eigenvalues calculation, etc.
I stress the "space ...
4
votes
0answers
263 views
The problem of whether or not every function computable in time $T(n)$ is computable in time $T(n)^{O(1)}$ and space $T(n)^{o(1)}$ simultaneously
If a function is computable in time $T(n)$, is it computable in time $T(n)^{O(1)}$ and space $T(n)^{o(1)}$ simultaneously?
We won't be able to prove it, because it implies the open problems $\text{P} ...
17
votes
1answer
945 views
Quadratic relationship between nondeterministic and deterministic space?
Savitch's theorem shows that $\mathrm{NSPACE}(f(n)) \subseteq \mathrm{DSPACE}(f(n)^2)$ for all large enough functions $f$, and proving that this is tight has been an open problem for decades.
Suppose ...
7
votes
2answers
343 views
Are space and time hierarchies even comparable?
I am wondering if there are any results to what extent the space and time hierarchies "disagree" on which problem is harder. For example, is it known whether there are languages $L_1$ and $L_2$ such ...
6
votes
1answer
160 views
Is $L \subset 1NL$ when $L \neq NL$?
A log-space Turing machine has a read-only input tape, a write-only output tape and uses at most $O(\log n)$ space in its read-write work tapes. The classes $L$ and $NL$ contain those languages which ...
6
votes
0answers
365 views
PSPACE completeness, with different kinds of reductions
PSPACE-complete$_{FP}$ problems are the PSPACE problems such that every other PSPACE problem can be transformed to it with a polynomial time reduction, i.e. the reduction is an algorithm $\in$ FP. ...
5
votes
0answers
845 views
Any known connections between open problems for time and space: P vs L, NP vs NL, BPP vs BPL, ⊕P vs ⊕L
It would be nice to show that $P=L$ implies $NP=NL$. Or, $NP=NL$ implies $UP=UL$. Or maybe, $⊕P = ⊕L$ implies $PP = PL$.
Are there any known connections between the problems: P vs L, UP vs UL, NP ...
0
votes
0answers
192 views
$CH=UL$ and partial breaking of transitive closure bottleneck problem and Savitch's theorem?
Let $L^t=DSPACE[O(\log n)^t]$, $NL^t=NSPACE[O(\log n)^t]$ and $UL^t=USPACE[O(\log n)^t$.
Savitch provides $NL\subseteq L^{2}$.
If $CH=UL$ we clearly got rid of the transitive closure bottleneck ...
4
votes
2answers
169 views
Function with space-depending computation time
Does a function exist which is easily computable for one space capacity and is hard to compute for another? I am looking for a function which can be computed in polytime when available space is at ...
