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Inclusion problems for patterns with a bounded number of variables

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posted on 2017-09-19, 14:56 authored by Joachim Bremer, Dominik FreydenbergerDominik Freydenberger
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 [D.D. Freydenberger, D. Reidenbach, Bad news on decision problems for patterns, Information and Computation 208 (1) (2010) 83-96] 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. © 2012 Elsevier Inc.

Funding

Joachim Bremer was supported by the German Research Foundation (DFG) [grant SCHW 837/3-3].

History

School

  • Science

Department

  • Computer Science

Published in

Information and Computation

Volume

220-221

Pages

15 - 43

Citation

BREMER, J. and FREYDENBERGER, D.D., 2012. Inclusion problems for patterns with a bounded number of variables. Information and Computation, 220-221, pp.15-43

Publisher

© Elsevier Inc.

Version

  • 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

2012

Notes

A preliminary version of this article appeared at Developments in Language Theory: DLT 2010.

ISSN

0890-5401

eISSN

1090-2651

Language

  • en

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