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@InProceedings
Beitrag in Tagungsband, Workshop

Author, Editor
Author(s):
Jez, Arturdblp
Editor(s):
Portier, Natacha
Wilke, Thomas
dblp
dblp
Not MPII Editor(s):
Portier, Natacha
Wilke, Thomas
BibTeX cite key*:
Jez2013STACS
Title, Booktitle
Title*:
Recompression: a simple and powerful technique for word equations
25.pdf (532.37 KB)
Booktitle*:
30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)
Event, URLs
Conference URL::
http://www.stacs2013.uni-kiel.de/
Downloading URL:
http://drops.dagstuhl.de/opus/volltexte/2013/3937
Event Address*:
Kiel, Germany
Language:
English
Event Date*
(no longer used):
Organization:
Event Start Date:
27 February 2013
Event End Date:
2 March 2013
Publisher
Name*:
Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik
URL:
http://www.dagstuhl.de/publikationen/
Address*:
Dagstuhl, Germany
Type:
Vol, No, Year, pp.
Series:
Leibniz International Proceedings in Informatics (LIPIcs)
Volume:
20
Number:
Month:
February
Pages:
233-244
Year*:
2013
VG Wort Pages:
ISBN/ISSN:
978-3-939897-50-7
Sequence Number:
DOI:
10.4230/LIPIcs.STACS.2013.233
Note, Abstract, ©
(LaTeX) Abstract:
We present an application of a local recompression technique,
previously developed by the author in the context of compressed membership problems
and compressed pattern matching, to word equations.
The technique is based on local modification of variables (replacing $X$ by $aX$ or $Xa$)
and replacement of pairs of letters appearing in the equation by a `fresh' letter,
which can be seen as a bottom-up compression of the solution
of the given word equation, to be more specific, building an SLP (Straight-Line Programme)
for the solution of the word equation.


Using this technique we give new self-contained
proofs of many known results for word equations:
the presented nondeterministic algorithm
runs in $O(n \log n)$ space and in time polynomial in $\log N$ and $n$,
where $N$ is the size of the length-minimal solution of the word equation.
It can be easily generalised
to a generator of all solutions of the word equation.
A further analysis of the algorithm yields a doubly exponential
upper bound on the size of the length-minimal solution.
The presented algorithm does not use
exponential bound on the exponent of periodicity.
Conversely, the analysis of the algorithm yields
a new proof of the exponential bound on exponent of periodicity.
For $O(1)$ variables with arbitrary many appearances
it works in linear space.
Keywords:
Word equations, exponent of periodicity, string unification
Download
Access Level:
Public

Correlation
MPG Unit:
Max-Planck-Institut für Informatik
MPG Subunit:
Algorithms and Complexity Group
External Affiliations:
Institute of Computer Science, University of Wroclaw
Audience:
popular
Appearance:
MPII WWW Server, MPII FTP Server, MPG publications list, university publications list, working group publication list, Fachbeirat, VG Wort



BibTeX Entry:

@INPROCEEDINGS{Jez2013STACS,
AUTHOR = {Jez, Artur},
EDITOR = {Portier, Natacha and Wilke, Thomas},
TITLE = {Recompression: a simple and powerful technique for word equations},
BOOKTITLE = {30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)},
PUBLISHER = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
YEAR = {2013},
VOLUME = {20},
PAGES = {233--244},
SERIES = {Leibniz International Proceedings in Informatics (LIPIcs)},
ADDRESS = {Kiel, Germany},
MONTH = {February},
ISBN = {978-3-939897-50-7},
DOI = {10.4230/LIPIcs.STACS.2013.233},
}


Entry last modified by Artur Jez, 02/17/2014
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Editor(s)
[Library]
Created
02/25/2013 04:14:01 PM
Revisions
2.
1.
0.

Editor(s)
Artur Jez
Artur Jez
Artur Jez

Edit Dates
01/21/2014 03:15:44 PM
01/21/2014 03:14:28 PM
02/25/2013 04:14:01 PM


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