Uniform generation of infinite traces-Reference-Cited by-同舟云学术

Uniform generation of infinite traces

Published:2022-06-01 Issue:1 Volume:30 Page:1-7
ISSN:1788-800X
Container-title:Pure Mathematics and Applications
language:en
Short-container-title:

Author:

Abbes Samy¹,Jugé Vincent²

Affiliation:

1. Université Paris Cité , IRIF CNRS UMR 8243 , 8 place Aurélie Nemours , Paris , France

2. Univ Gustave Eiffel , CNRS, LIGM , F-77454 Marne-la-Vallée , France

Abstract

Abstract We introduce an algorithm for the uniform generation of infinite traces, i.e., infinite words up to commutation of some letters. The algorithm outputs on-the-fly approximations of a theoretical infinite trace, the latter being distributed according to the exact uniform probability measure. The average size of the approximation grows linearly with the time of execution of the algorithm, provided that some–costly–precomputations have been done.

Publisher

Walter de Gruyter GmbH

Link

https://www.sciendo.com/pdf/10.2478/puma-2022-0002

Reference12 articles.

1. [1] X. Viennot, Heaps of pieces, I: basic definitions and combinatorial lemmas, in: Labelle, G. and Leroux, P. (Eds.), Combinatoire énumérative, Lecture Notes in Math., 1234 (1986) 321–350.

2. [2] P. Cartier and D. Foata, Problèmes combinatoires de commutation et réarrangements, Lecture Notes in Math., 85 (1969).10.1007/BFb0079468

3. [3] S. Abbes and J. Mairesse, Uniform and Bernoulli measures on the boundary of trace monoids, J. Combin. Theory Ser. A, 135 (2015) 201–236.

4. [4] S. Abbes and J. Mairesse, Uniform generation in trace monoids, in: Italiano, G., Pighizzini, G. and Sannella, D. (Eds.), Mathematical Foundations of Computer Science 2015 (MFCS 2015), Lecture Notes in Comput. Sci., 9234 (2015) 63–75.

5. [5] C. Krattenthaler, The theory of heaps and the Cartier-Foata monoid, in Electronic reed-ition of “Problèmes combinatoires de commutation et rárrangements”, pp. 63–73, EMIS, 2006.