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Pumping, with or Without Choice

  • Aquinas Hobor
  • Elaine LiEmail author
  • Frank Stephan
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11893)

Abstract

We present the first machine-checked formalization of Jaffe and Ehrenfeucht, Parikh and Rozenberg’s (EPR) pumping lemmas in the Coq proof assistant. We formulate regularity in terms of finite derivatives, and prove that both Jaffe’s pumping property and EPR’s block pumping property precisely characterize regularity. We illuminate EPR’s classical proof that the block cancellation property implies regularity, and discover that—as best we can tell—their proof relies on the Axiom of Choice. We provide a new proof which eliminates the use of Choice. We explicitly construct a function which computes block cancelable languages from well-formed short languages.

Keywords

Pumping lemmas Axiom of Choice Coq 

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Yale-NUS CollegeSingaporeSingapore
  2. 2.School of Computing, National University of SingaporeSingaporeSingapore
  3. 3.Department of MathematicsNational University of SingaporeSingaporeSingapore

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