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|Title: ||Inclusion problems for patterns with a bounded number of variables|
|Authors: ||Bremer, Joachim|
Freydenberger, Dominik D.
|Issue Date: ||2010|
|Publisher: ||© Springer-Verlag Berlin Heidelberg|
|Citation: ||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.100-111|
|Series/Report no.: ||Lecture Notes in Computer Science; 6224|
|Abstract: ||We 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.|
|Description: ||The final publication is available at Springer via https://doi.org/10.1007/978-3-642-14455-4_11|
|Version: ||Accepted for publication|
|Publisher Link: ||http://dx.doi.org/10.1007/978-3-642-14455-4_11|
|Appears in Collections:||Published Articles (Computer Science)|
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