Lambda terms of bounded unary height

8th Workshop on Analytic Algorithmics and Combinatorics 2011, ANALCO 2011

Volumn , Issue , 2011, Pages 23-32

  Bodini, Olivier ^a,b   Gardy, Danièle ^c   Gittenberger, Bernhard ^d  

^a UNIVERSITÉ PIERRE ET MARIE CURIE   (France)

^b UNIVERSITÉ PARIS DIDEROT   (France)

^c UNIVERSITY OF VERSAILLES   (France)

^d INSTITUT FÜR DISKRETE MATHEMATIK UND GEOMETRIE   (Austria)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC ENUMERATIONS; BOLTZMANN; GENERATING FUNCTION APPROACH; GENERATING FUNCTIONS; LAMBDA TERMS; RANDOM GENERATION; SINGULARITY ANALYSIS; SQUARE ROOTS;

COMBINATORIAL MATHEMATICS;

EID: 84959884125     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1137/1.9781611973013.3     Document Type: Conference Paper

References (31)

1. Alfred V. Aho and Neil J. A. Sloane. Some Doubly Exponential Sequences. Fibonacci Quarterly, Vol. 11 (1970), pp. 429-437.
2. th GASCOM workshop, Montrèal (Canada), September 2-4, 2010.
3. th international Conference on Lattice Paths and Applications, Siena (Italy), July 4-7, 2010.
4. th GASCOM workshop, Bibbiena (Italy), June 16-19, 2008.
5. Olivier Bodini and Yann Ponty, Multi-dimensional Boltzmann sampling of languages, Conference on Analysis of Algorithms, A of A'10, Vienna (Austria), June 28-July 2, 2010.
6. Manuel Bodirsky, Eric Fusy, Mihyun Kang, and Stefan Vigerske, An unbiased pointing operator for unlabeled structures, with applications to counting and sampling, SODA '07: Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms (Philadelphia, PA, USA), Society for Industrial and Applied Mathematics, 2007, pp. 356-365.
7. Miklós Bóna and Philippe Flajolet, Isomorphism and Symmetries in Random Phylogenesc Trees, Journal of Applied Probability, vol 46 (2009), pp. 1005-1019.
8. Jérémie Bouttier and Emmanuel Guitter, Planar maps and continued fractions, preprint, arXiv:1007:0419, 2010.
9. Alonzo Church. An Unsolvable Problem of Elementary Number Theory. Amer. J. Math., 58(2):345-363, 1936.
10. René David, Katarzyna Grygiel, Jakub Kozik, Christophe Raffalli, Guillaume Theyssier, and Marek Zaionc. Asymptotically almost all λ-terms are strongly normalizing. Preprint, arXiv:math.LO/0903.5505, 2010.
11. René David and Marek Zaionc. Counting proofs in propositional logic. Arch. Math. Logic, 48(2):185-199, 2009.
12. Philippe Duchon, Philippe Flajolet, Guy Louchard, and Gilles Schaeffer, Boltzmann samplers for the random generation of combinatorial structures, Combinatorics, Probablity, and Computing 13 (2004), no. 4-5, 577-625, Special issue on Analysis of Algorithms.
13. Philippe Flajolet, Combinatorial aspects of continued fractions, Discrete Mathematics 32 (1980), 125-161.
14. Reprinted in the 35th Special Anniversary Issue of Discrete Mathematics, Volume 306, Issue 1011, Pages 992-1021 (2006).
15. Philippe Flajolet, Eric Fusy, and Carine Pivoteau, Boltzmann sampling of unlabelled structures, Proceedings of ANALCO'07 (Analytic Combinatorics and Algorithms) Conference (SIAM Press, ed.), Vol. 126, 2007, pp. 201-211.
16. Philippe Flajolet and Andrew Odlyzko. Singularity analysis of generating functions. SIAM Journal on Discrete Mathematics, 3(2):216-240, 1990.
17. Philippe Flajolet and Robert Sedgewick. Analytic combinatorics. Cambridge University Press, Cambridge, 2009.
18. Philippe Flajolet, Paul Zimmerman, and Bernard Van Cutsem, A calculus for the random generation of labelled combinatorial structures, Theoretical Computer Science 132 (1994), no. 1-2, 1-35.
19. Herve Fournier, Daniéle Gardy, Antoine Genitrini, and Bernhard Gittenberger. Complexity and limiting ratio of Boolean functions over implication. In Proceedings of the 33rd International Symposium on Mathematical Foundations of Computer Science, Volume 5162/2008 of Lecture Notes in Comput. Sci., pages 347-262. Springer, 2008.
20. Antoine Genitrini, Jakub Kozik, and Marek Zaionc. Intuitionistic vs. classical tautologies, quantitative comparison. In Types for proofs and programs, Volume 4941 of Lecture Notes in Comput. Sci., pages 100-109. Springer, Berlin, 2008.
21. J. Roger Hindley. BCK and BCI logics, condensed detachment and the 2-property. Notre Dame J. Formal Logic, 34(2):231-250, 1993.
22. Yasuyuki Imai and Kiyoshi Iséki. Corrections to: "On axiom systems of propositional calculi. I". Proc. Japan Acad., 41:669, 1965.
23. Yasuyuki Imai and Kiyoshi Iséki. On axiom systems of propositional calculi. I. Proc. Japan Acad., 41:436-439, 1965.
24. Kiyoshi Iséki and Shôtarô Tanaka. An introduction to the theory of BCK-algebras. Math. Japon., 23(1):1-26, 1978/79.
25. Stephen C. Kleene. A Theory of Positive Integers in Formal Logic. Part I. Amer. J. Math., 57(1):153-173, 1935.
26. Stephen C. Kleene. A Theory of Positive Integers in Formal Logic. Part II. Amer. J. Math., 57(2):219-244, 1935.
27. Albert Nijenhuis and Herbert S. Wilf, Combinatorial algorithms, Academic Press, 1978.
28. Richard Otter, The number of trees, Ann. of Math. 49 (3), 583-599, 1948.
29. Carine Pivoteau, Bruno Salvy, and Michèle Soria, Boltzmann oracle for combinatorial systems, Algorithms, Trees, Combinatorics and Probabilities, Discrete Mathematics and Theoretical Computer Science, 2008, Proceedings of the Fifth Colloquium on Mathematics and Computer Science. Blaubeuren, Germany. September 22-26, 2008, pp. 475-488.
30. Olivier Roussel and Michèle Soria, Boltzmann sampling of ordered structures, Electronic Notes in Discrete Mathematics 35 (2009), 305-310.
31. Marek Zaionc. On the asymptotic density of tautologies in logic of implication and negation. Reports on Mathematical Logic Vol. 39, 67-87, 2005.