Abstract
In this paper, a compressed membership problem for finite automata, both deterministic (DFAs) and nondeterministic (NFAs), with compressed transition labels is studied. The compression is represented by straightline programs (SLPs), i.e. contextfree grammars generating exactly one string. A novel technique of dealing with SLPs is introduced: the SLPs are recompressed, so that substrings of the input text are encoded in SLPs labelling the transitions of the NFA (DFA) in the same way, as in the SLP representing the input text. To this end, the SLPs are locally decompressed and then recompressed in a uniform way. Furthermore, in order to reflect the recompression in the NFA, we need to modify it only a little, in particular its size stays polynomial in the input size.
Using this technique it is shown that the compressed membership for NFA with compressed labels is in NP, thus confirming the conjecture of Plandowski and Rytter [Plandowski Rytter 1999] and extending the partial result of Lohrey and Mathissen [Lohrey and Mathissen 2011];
as this problem is known to be NPhard, we settle its exact computational complexity. Moreover, the same technique applied to the compressed membership for DFA with compressed labels yields that this problem is in P, and this problem is known to be Phard.
BibTeX  Entry
@InProceedings{jez:LIPIcs:2012:3406,
author = {Artur Jez},
title = {{Compressed Membership for NFA (DFA) with Compressed Labels is in NP (P)}},
booktitle = {29th International Symposium on Theoretical Aspects of Computer Science (STACS 2012)},
pages = {136147},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {9783939897354},
ISSN = {18688969},
year = {2012},
volume = {14},
editor = {Christoph D{\"u}rr and Thomas Wilke},
publisher = {Schloss DagstuhlLeibnizZentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2012/3406},
URN = {urn:nbn:de:0030drops34068},
doi = {10.4230/LIPIcs.STACS.2012.136},
annote = {Keywords: Compressed membership problem, SLP, Finite Automata, Algorithms for compressed data}
}
Keywords: 

Compressed membership problem, SLP, Finite Automata, Algorithms for compressed data 
Collection: 

29th International Symposium on Theoretical Aspects of Computer Science (STACS 2012) 
Issue Date: 

2012 
Date of publication: 

24.02.2012 