2010 DLT - Inclusion Problems for Patterns With a Bounded Number of Variables.pdf (186.17 kB)
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posted on 2017-09-19, 13:56 authored by Joachim Bremer, Dominik FreydenbergerDominik FreydenbergerWe study the inclusion problems for pattern languages that are generated by patterns with a bounded number of variables. This continues the work by Freydenberger and Reidenbach (Information and Computation 208 (2010)) by showing that restricting the inclusion problem to significantly more restricted classes of patterns preserves undecidability, at least for comparatively large bounds. For smaller bounds, we prove the existence of classes of patterns with complicated inclusion relations, and an open inclusion problem, that are related to the Collatz Conjecture. In addition to this, we give the first proof of the undecidability of the inclusion problem for NE-pattern languages that, in contrast to previous proofs, does not rely on the inclusion problem for E-pattern languages, and proves the undecidability of the inclusion problem for NE-pattern languages over binary and ternary alphabets. © 2010 Springer-Verlag Berlin Heidelberg.
History
School
- Science
Department
- Computer Science
Published in
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)Volume
6224 LNCSPages
100 - 111Citation
BREMER, J. and FREYDENBERGER, D.D., 2010. Inclusion problems for patterns with a bounded number of variables. IN: Gao Y., Lu H., Seki S., Yu S. (eds). Developments in Language Theory. DLT 2010. Lecture Notes in Computer Science, vol 6224. Springer: Berlin, Heidelberg, pp.100-111Publisher
© Springer-Verlag Berlin HeidelbergVersion
- AM (Accepted Manuscript)
Publisher statement
This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/Publication date
2010Notes
The final publication is available at Springer via https://doi.org/10.1007/978-3-642-14455-4_11ISBN
3642144543;9783642144554;9783642144547ISSN
0302-9743eISSN
1611-3349Publisher version
Book series
Lecture Notes in Computer Science; 6224Language
- en