Ruzzo-Simon-Tompa oracle access mechanism
In a paper on relativizing logspace computations, Ladner and Lynch construct an oracle relative to which $mathsf{NL} nsubseteq mathsf{P}$. There are some more pathological examples in this vein in the...
View ArticleWhat are the consequences of $L = oplus L$?
Shiva Kintali has just announced a (cool!) result that graph isomorphism for bounded treewidth graphs of width $geq 4$ is $oplus L$-hard. Informally, my question is, “How hard is that?” We know that...
View ArticleA super-linear time problem in NL
It is a well-known fact that $ mathsf{NL} = cup_{k>0} mathsf{2NFA[k]} $, where $ mathsf{2NFA[k]} $ is the class of languages recognized by two-way nondeterministic finite automata with $ k>0 $...
View ArticleTreewidth and the NL vs L Problem
ST-Connectivity is the problem of determining whether there exists a directed path between two distinguished vertices $s$ and $t$ in a directed graph $G(V,E)$. Whether this problem can be solved in...
View ArticleHardness of Computing Weisfeiler-Lehman labels
The 1-dim Weisfeiler-Lehman algorithm (WL) is commonly known as canonical labeling or color refinement algorithm. It works as follows : The initial coloring $C_0$ is uniform, $C_0(v) = 1$ for all...
View ArticleTwo way deterministic multihead counter automata or logspace TM with counter
Is that known something about languages recognized by two-way deterministic multihead counter automaton or logspace TM with counter (equivalent model)? This class called Aux2DC in my advisor’s paper....
View ArticleCan we show that $mathsf{NL}^mathsf{NL} = mathsf{NL}$? [closed]
We know by Immerman–Szelepcsényi theorem that $mathsf{NL}=mathsf{coNL}$? Does it follow from this theorem that $mathsf{NL}^mathsf{NL} = mathsf{NL}$? Here, $mathsf{NL}^mathsf{NL}$ denotes the class of...
View ArticleWhat if an $mathsf L$-complete problem has $mathsf{NC}^1$ circuits?
In other words, is there a result comparable to the Karp-Lipton theorem starting from the assumption $Linmathsf{NC}^1/mathsf{poly}$ with $L$ an $mathsf L$-complete language (under, say, $mathsf{AC}^0$...
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 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 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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