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On Computability and Learnability of the Pumping Lemma Function

  • Dariusz Kalociński
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8370)

Abstract

On the basis of the well known pumping lemma for regular languages we define such a partial function f: \({\mbox{I\!N}} \rightarrow{\mbox{I\!N}}\) that for every e it yields the least pumping constant for the language W e . We ask whether f is computable. Not surprisingly f turns out to be non-computable. Then we check whether f is algorithmically learnable. This is also proved not to be the case. Further we investigate how powerful oracle is necessary to actually learn f. We prove that f is learnable in 0′. We also prove some facts relating f to arithmetical hierarchy.

Keywords

pumping lemma computability algorithmic learning arithmetical hierarchy reducibility 

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Dariusz Kalociński
    • 1
  1. 1.Institute of PhilosophyUniversity of WarsawWarsawPoland

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