Structural Complexity Theory

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19
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What is the power of general poly-size permutation branching programs?

Call $\mathsf{PPBP}$ the class of languages decided by poly-size families of permutation branching programs, which are layered branching programs (i.e., the ones defined here) whose transitions ...
14
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1answer
283 views

$\mathsf{EXP}$ vs $\oplus\mathsf{EXP}$

In our recent work, we resolve a computational problem which arose in combinatorial context, under assumption that $\mathsf{EXP} \ne \mathsf{\oplus{}EXP}$, where $\mathsf{\oplus{}EXP}$ is the ...
4
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119 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 ...
3
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91 views

Symmetry of optimal solutions to discrete optimization problems

Given a graph, say one wants to find the clique number, independence number, chromatic number, vertex cover number etc., one knows that a solution exists. However if the solution space has more than ...
8
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1answer
120 views

Can $\log^k n$ alternations be simulated in $\mathsf{NC}^k$?

Let $\mathsf{ATISP}(f(n), g(n))$ be the class of languages decided by alternating Turing machines that halt in time $f(n)$ using space $g(n)$. Let $\mathsf{AALTSP}(f(n), g(n))$ be the class of ...
33
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0answers
662 views

What are the consequences of $\mathsf{L}^2 \subseteq \mathsf{P}$?

We know that $\mathsf{L} \subseteq \mathsf{NL} \subseteq \mathsf{P}$ and that $\mathsf{L} \subseteq \mathsf{NL} \subseteq \mathsf{L}^2 \subseteq $ $\mathsf{polyL}$, where $\mathsf{L}^2 = ...
21
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1answer
776 views

Algorithms and structural complexity theory

Many important results in computational complexity theory, and in particular "structural" complexity theory, have the interesting property that they can be understood as fundamentally following (as I ...
15
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1answer
265 views

Strongly Regular Graph and GI-Completeness

It is not known if graph isomorphism (GI) for strongly regular graphs (SRGs) is in P. Are there any hints that it might or might not be GI-Complete? Are there any strong consequences in such cases? ...
9
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1answer
592 views

Does $\mathsf{EXP}=\mathsf{NEXP}$ imply $\mathsf{E}=\mathsf{NE}$?

Does $\mathsf{EXP}=\mathsf{NEXP}$ imply $\mathsf{E}=\mathsf{NE}$?
17
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3answers
678 views

How Hard is Exact Simulation of Algorithms, and a Related Operation on Complexity Classes

Teaser Since the problem is longish here is a special case that capture its essense. Problem: Let A be a detrministic algorithm for 3-SAT. Is the problem of completely simulating the algorithm ...
13
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1answer
1k views

What are the classic papers from the recursion theoretic area of complexity theory?

Two papers I would include are: D. Kozen, "Indexing of subrecursive classes", STOC, 1978. R. Ladner, "On the Structure of Polynomial Time Reducibility", JACM, 1975.