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arXiv · 2007.06327

Generating Functions for Probabilistic Programs

Lutz Klinkenberg·Kevin Batz·Benjamin Lucien Kaminski·Joost-Pieter Katoen·Joshua Moerman·Tobias Winkler
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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.

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Lutz Klinkenberg, Kevin Batz, Benjamin Lucien Kaminski, Joost-Pieter Katoen, Joshua Moerman, Tobias Winkler. 2020-07-13. Generating Functions for Probabilistic Programs. https://arxiv.org/abs/2007.06327

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