Does ${bf AC^0PAD} = {bf PPAD}$?
What happens if we define ${bf PPAD}$ such that instead of a polytime Turing-machine/polysize circuit, a logspace Turing-machine or an ${bf AC^0}$ circuit encodes the problem? Recently giving faster...
View ArticleWhat if an $mathsf L$-complete problem has $mathsf{NC}^1$ circuits? More...
Edit: let me reformulate the question in a more specific way (and change the title accordingly). A slightly edited version of the original question follows. Is there a result comparable to the...
View ArticleDoes ${bf AC^0PAD} = {bf PPAD}$?
What happens if we define ${bf PPAD}$ such that instead of a polytime Turing-machine/polysize circuit, a logspace Turing-machine or an ${bf AC^0}$ circuit encodes the problem? Recently giving faster...
View ArticleWhat if an $mathsf L$-complete problem has $mathsf{NC}^1$ circuits? More...
Edit: let me reformulate the question in a more specific way (and change the title accordingly). A slightly edited version of the original question follows. Is there a result comparable to the...
View ArticleWhat if an $mathsf L$-complete problem has $mathsf{NC}^1$ circuits? More...
Edit: let me reformulate the question in a more specific way (and change the title accordingly). A slightly edited version of the original question follows. Is there a result comparable to the...
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Any known connections between open problems for time and space: P vs L, NP vs...
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 vs...
View ArticleDetecting undirected cycles in logarithmic space [closed]
I have a lot of difficulties with constructing algorithms that use $O(log n)$ space, as I am unsure about how much can be stored on the worktape. I am trying to figure out an algorithm for the problem:...
View ArticleDoes ${bf AC^0PAD} = {bf PPAD}$?
What happens if we define ${bf PPAD}$ such that instead of a polytime Turing-machine/polysize circuit, a logspace Turing-machine or an ${bf AC^0}$ circuit encodes the problem? Recently giving faster...
View ArticleComplexity of the search version of 2-SAT assuming $mathsf{L = NL}$
If $mathsf{L = NL}$, then there is a logspace algorithm that solves the decision version of 2-SAT. Is $mathsf{L = NL}$ known to imply that there is a logspace algorithm to obtain a satisfying...
View ArticleWhat is the space complexity of computing the eigenvectors of a matrix?
By the answer to this question, computing the eigenvalues of a matrix to within $2^{-n}$ precision can be done in polylogarithmic space. Is it also possible to compute the eigenvectors of a matrix to...
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