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Ketema, J. and Simonsen, J.G. (2012) Characterizing Languages by Normalization and Termination in String Rewriting. In: Proceedings of the 16th International Conference on Developments in Language Theory (DLT 2012), 14-17 Aug 2012, Taipei, Taiwan. pp. 459-464. Lecture Notes in Computer Science 7410. Springer Verlag. ISSN 0302-9743 ISBN 978-3-642-31652-4
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Official URL: http://dx.doi.org/10.1007/978-3-642-31653-1_41
We characterize sets of strings using two central properties from rewriting: normalization and termination. We recall the well-known result that any recursively enumerable set of strings can occur as the set of normalizing strings over a “small” alphabet if the rewriting system is allowed access to a “larger” alphabet (and extend the result to termination). We then show that these results do not hold when alphabet extension is disallowed. Finally, we prove that for every reasonably well-behaved deterministic time complexity class, there is a set of strings complete for the class that also occurs as the set of normalizing or terminating strings, without alphabet extension.
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