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)


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.


Normal Form Transitive Closure Deterministic Turing Machine Term Rewrite System Thue System 
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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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