Unary profile of lambda terms with restricted De Bruijn indices - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Discrete Mathematics and Theoretical Computer Science Année : 2021

Unary profile of lambda terms with restricted De Bruijn indices

Résumé

In this paper we present an average-case analysis of closed lambda terms with restricted values of De Bruijn indices in the model where each occurrence of a variable contributes one to the size. Given a fixed integer k, a lambda term in which all De Bruijn indices are bounded by k has the following shape: It starts with k De Bruijn levels, forming the so-called hat of the term, to which some number of k-colored Motzkin trees are attached. By means of analytic combinatorics, we show that the size of this hat is constant on average and that the average number of De Bruijn levels of k-colored Motzkin trees of size n is asymptotically Θ(√ n). Combining these two facts, we conclude that the maximal non-empty De Bruijn level in a lambda term with restrictions on De Bruijn indices and of size n is, on average, also of order √ n. On this basis, we provide the average unary profile of such lambda terms.
Fichier principal
Vignette du fichier
Unary_height_of_lambda_terms.pdf (404.21 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-02313735 , version 1 (11-10-2019)
hal-02313735 , version 2 (04-08-2020)
hal-02313735 , version 3 (21-01-2021)

Identifiants

Citer

Katarzyna Grygiel, Isabella Larcher. Unary profile of lambda terms with restricted De Bruijn indices. Discrete Mathematics and Theoretical Computer Science, 2021, vol. 22 no. 3, Computational Logic and Applications (CLA'19), ⟨10.46298/dmtcs.5836⟩. ⟨hal-02313735v3⟩
120 Consultations
572 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More