7,647 research outputs found
Graph Spectral Properties of Deterministic Finite Automata
We prove that a minimal automaton has a minimal adjacency matrix rank and a
minimal adjacency matrix nullity using equitable partition (from graph spectra
theory) and Nerode partition (from automata theory). This result naturally
introduces the notion of matrix rank into a regular language L, the minimal
adjacency matrix rank of a deterministic automaton that recognises L. We then
define and focus on rank-one languages: the class of languages for which the
rank of minimal automaton is one. We also define the expanded canonical
automaton of a rank-one language.Comment: This paper has been accepted at the following conference: 18th
International Conference on Developments in Language Theory (DLT 2014),
August 26 - 29, 2014, Ekaterinburg, Russi
Building Efficient and Compact Data Structures for Simplicial Complexes
The Simplex Tree (ST) is a recently introduced data structure that can
represent abstract simplicial complexes of any dimension and allows efficient
implementation of a large range of basic operations on simplicial complexes. In
this paper, we show how to optimally compress the Simplex Tree while retaining
its functionalities. In addition, we propose two new data structures called the
Maximal Simplex Tree (MxST) and the Simplex Array List (SAL). We analyze the
compressed Simplex Tree, the Maximal Simplex Tree, and the Simplex Array List
under various settings.Comment: An extended abstract appeared in the proceedings of SoCG 201
The Rabin index of parity games
We study the descriptive complexity of parity games by taking into account
the coloring of their game graphs whilst ignoring their ownership structure.
Colored game graphs are identified if they determine the same winning regions
and strategies, for all ownership structures of nodes. The Rabin index of a
parity game is the minimum of the maximal color taken over all equivalent
coloring functions. We show that deciding whether the Rabin index is at least k
is in PTIME for k=1 but NP-hard for all fixed k > 1. We present an EXPTIME
algorithm that computes the Rabin index by simplifying its input coloring
function. When replacing simple cycle with cycle detection in that algorithm,
its output over-approximates the Rabin index in polynomial time. Experimental
results show that this approximation yields good values in practice.Comment: In Proceedings GandALF 2013, arXiv:1307.416
Fast and Tiny Structural Self-Indexes for XML
XML document markup is highly repetitive and therefore well compressible
using dictionary-based methods such as DAGs or grammars. In the context of
selectivity estimation, grammar-compressed trees were used before as synopsis
for structural XPath queries. Here a fully-fledged index over such grammars is
presented. The index allows to execute arbitrary tree algorithms with a
slow-down that is comparable to the space improvement. More interestingly,
certain algorithms execute much faster over the index (because no decompression
occurs). E.g., for structural XPath count queries, evaluating over the index is
faster than previous XPath implementations, often by two orders of magnitude.
The index also allows to serialize XML results (including texts) faster than
previous systems, by a factor of ca. 2-3. This is due to efficient copy
handling of grammar repetitions, and because materialization is totally
avoided. In order to compare with twig join implementations, we implemented a
materializer which writes out pre-order numbers of result nodes, and show its
competitiveness.Comment: 13 page
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