Characterizing Languages by Normalization and Termination in String Rewriting

(Extended Abstract)
  • Jeroen Ketema
  • Jakob Grue Simonsen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7410)

Abstract

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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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Jeroen Ketema
    • 1
  • Jakob Grue Simonsen
    • 2
  1. 1.Faculty EEMCSUniversity of TwenteEnschedeThe Netherlands
  2. 2.Department of Computer ScienceUniversity of Copenhagen (DIKU)Copenhagen SDenmark

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