Flavien Breuvart ; Ugo Dal Lago ; Agathe Herrou - On Higher-Order Probabilistic Subrecursion

lmcs:4226 - Logical Methods in Computer Science, December 23, 2021, Volume 17, Issue 4 - https://doi.org/10.46298/lmcs-17(4:25)2021
On Higher-Order Probabilistic Subrecursion

Authors: Flavien Breuvart ; Ugo Dal Lago ; Agathe Herrou

We study the expressive power of subrecursive probabilistic higher-order calculi. More specifically, we show that endowing a very expressive deterministic calculus like Gödel's $\mathbb{T}$ with various forms of probabilistic choice operators may result in calculi which are not equivalent as for the class of distributions they give rise to, although they all guarantee almost-sure termination. Along the way, we introduce a probabilistic variation of the classic reducibility technique, and we prove that the simplest form of probabilistic choice leaves the expressive power of $\mathbb{T}$ essentially unaltered. The paper ends with some observations about the functional expressive power: expectedly, all the considered calculi capture the functions which $\mathbb{T}$ itself represents, at least when standard notions of observations are considered.

Volume: Volume 17, Issue 4
Published on: December 23, 2021
Accepted on: October 14, 2020
Submitted on: January 22, 2018
Keywords: Computer Science - Logic in Computer Science