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Electronic Colloquium on Computational Complexity

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Reports tagged with dot-depth hierarchy:
TR04-011 | 16th January 2004
Christian Glaßer

Counting with Counterfree Automata

We study the power of balanced regular leaf-languages.
First, we investigate (i) regular languages that are
polylog-time reducible to languages in dot-depth 1/2 and
(ii) regular languages that are polylog-time decidable.
For both classes we provide

- forbidden-pattern characterizations, and
- characterizations in terms of regular expressions.

Both ... more >>>

TR05-035 | 24th March 2005
Christian Glaßer, Stephen Travers, Klaus W. Wagner

A Reducibility that Corresponds to Unbalanced Leaf-Language Classes

We introduce the polynomial-time tree reducibility
(ptt-reducibility). Our main result states that for
languages $B$ and $C$ it holds that
$B$ ptt-reduces to $C$ if and only if
the unbalanced leaf-language class of $B$ is robustly contained in
the unbalanced leaf-language class of $C$.
... more >>>

TR07-094 | 3rd August 2007
Christian Glaßer, Heinz Schmitz, Victor Selivanov

Efficient Algorithms for Membership in Boolean Hierarchies of Regular Languages

The purpose of this paper is to provide efficient algorithms that decide membership for classes of several Boolean hierarchies for which efficiency (or even decidability) were previously not known. We develop new forbidden-chain characterizations for the single levels of these hierarchies and obtain the following results:

1. The classes of ... more >>>

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