Asymptotics and random sampling for BCI and BCK lambda terms

  • Authors:
  • O. Bodini;D. Gardy;A. Jacquot

  • Affiliations:
  • LIPN, Institut Galilée Université Paris Nord et CNRS UMR 7030, 99 avenue Jean-Baptiste Clément, 93430 Villetaneuse, France;PRISM, CNRS UMR 8144 et Université de Versailles Saint-Quentin en Yvelines, 45 avenue des Etats-Unis, 78035 Versailles Cedex, France;LIPN, Institut Galilée Université Paris Nord et CNRS UMR 7030, 99 avenue Jean-Baptiste Clément, 93430 Villetaneuse, France

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2013

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Abstract

This paper presents a bijection between combinatorial maps and a class of enriched trees, corresponding to a class of expression trees in some logical systems (constrained lambda terms). Starting from two alternative definitions of combinatorial maps: the classical definition by gluing half-edges, and a definition by non-ambiguous depth-first traversal, we derive non-trivial asymptotic expansions and efficient random generation of logic formulae (syntactic trees) in the BCI or BCK systems.