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Electronic Colloquium on Computational Complexity

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Reports tagged with hierarchy:
TR01-017 | 14th February 2001
Petr Savicky, Detlef Sieling

A Hierarchy Result for Read-Once Branching Programs with Restricted Parity Nondeterminism

Restricted branching programs are considered in complexity theory in
order to study the space complexity of sequential computations and
in applications as a data structure for Boolean functions. In this
paper (\oplus,k)-branching programs and (\vee,k)-branching
programs are considered, i.e., branching programs starting with a
... more >>>

TR01-101 | 14th December 2001
Philipp Woelfel

A Lower Bound Technique for Restricted Branching Programs and Applications

We present a new lower bound technique for two types of restricted
Branching Programs (BPs), namely for read-once BPs (BP1s) with
restricted amount of nondeterminism and for (1,+k)-BPs. For this
technique, we introduce the notion of (strictly) k-wise l-mixed
Boolean functions, which generalizes the concept of l-mixedness ... more >>>

TR09-025 | 11th March 2009
Arnaldo Moura, Igor Carboni Oliveira

A New Look at Some Classical Results in Computational Complexity

We propose a generalization of the traditional algorithmic space and
time complexities. Using the concept introduced, we derive an
unified proof for the deterministic time and space hierarchy
theorems, now stated in a much more general setting. This opens the
possibility for the unification and generalization of other results
that ... more >>>

TR10-136 | 26th August 2010
Arnab Bhattacharyya, Elena Grigorescu, Jakob Nordström, Ning Xie

Separations of Matroid Freeness Properties

Revisions: 1

Properties of Boolean functions on the hypercube that are invariant
with respect to linear transformations of the domain are among some of
the most well-studied properties in the context of property testing.
In this paper, we study a particular natural class of linear-invariant
properties, called matroid freeness properties. These properties ... more >>>

TR11-028 | 24th February 2011
Richard Beigel, Bin Fu

A Dense Hierarchy of Sublinear Time Approximation Schemes for Bin Packing

The bin packing problem is to find the minimum
number of bins of size one to pack a list of items with sizes
$a_1,\ldots , a_n$ in $(0,1]$. Using uniform sampling, which selects
a random element from the input list each time, we develop a
randomized $O({n(\log n)(\log\log n)\over ... more >>>

TR15-174 | 18th October 2015
Dmitry Itsykson, Alexander Knop, Dmitry Sokolov

Complexity of distributions and average-case hardness

We address a natural question in average-case complexity: does there exist a language $L$ such that for all easy distributions $D$ the distributional problem $(L, D)$ is easy on the average while there exists some more hard distribution $D'$ such that $(L, D')$ is hard on the average? We consider ... more >>>

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