Generating Functions for Probabilistic Programs
Logic in Computer Science
2020-07-14 v1 Programming Languages
Abstract
This paper investigates the usage of generating functions (GFs) encoding measures over the program variables for reasoning about discrete probabilistic programs. To that end, we define a denotational GF-transformer semantics for probabilistic while-programs, and show that it instantiates Kozen's seminal distribution transformer semantics. We then study the effective usage of GFs for program analysis. We show that finitely expressible GFs enable checking super-invariants by means of computer algebra tools, and that they can be used to determine termination probabilities. The paper concludes by characterizing a class of -- possibly infinite-state -- programs whose semantics is a rational GF encoding a discrete phase-type distribution.
Cite
@article{arxiv.2007.06327,
title = {Generating Functions for Probabilistic Programs},
author = {Lutz Klinkenberg and Kevin Batz and Benjamin Lucien Kaminski and Joost-Pieter Katoen and Joshua Moerman and Tobias Winkler},
journal= {arXiv preprint arXiv:2007.06327},
year = {2020}
}