A Cut-Free Cyclic Proof System for Kleene Algebra

  • Anupam Das
  • Damien PousEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10501)


We introduce a sound non-wellfounded proof system whose regular (or ‘cyclic’) proofs are complete for (in)equations between regular expressions. We achieve regularity by using hypersequents rather than usual sequents, with more structure in the succedent, and relying on the discreteness of rational languages to drive proof search. By inspection of the proof search space we extract a PSpace bound for the system, which is optimal for deciding such (in)equations.


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Univ. Lyon, CNRS, ENS de Lyon, UCB Lyon 1, LIPLyonFrance

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