Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6873944 | Information and Computation | 2015 | 19 Pages |
Abstract
In 2006, Varacca and Völzer proved that on finite graphs, Ï-regular large sets coincide with Ï-regular sets of probability 1, by using the existence of positional strategies in the related Banach-Mazur games. Motivated by this result, we try to understand relations between sets of probability 1 and various notions of simple strategies (including those introduced in a recent paper of Grädel and LeÃenich). Then, we introduce a generalisation of the classical Banach-Mazur game and in particular, a probabilistic version whose goal is to characterise sets of probability 1 (as classical Banach-Mazur games characterise large sets). We obtain a determinacy result for these games, when the winning set is a countable intersection of open sets.
Related Topics
Physical Sciences and Engineering
Computer Science
Computational Theory and Mathematics
Authors
Thomas Brihaye, Axel Haddad, Quentin Menet,