Year: 2023
Type: conference-paper
Abstract: Probabilistic pushdown automata (pPDA) are a natural operational model for a variety of recursive discrete stochastic processes. In this paper, we study certificates – succinct and easily verifiable proofs – for upper and lower bounds on various quantitative properties of a given pPDA. We reveal an intimate, yet surprisingly simple connection between the existence of such certificates and the expected time to termination of the pPDA at hand. This is established by showing that certain intrinsic properties, like the spectral radius of the Jacobian of the pPDA’s underlying polynomial equation system, are directly related to expected runtimes. As a consequence, we obtain that there always exist easy-to-check proofs for positive almost-sure termination: does a pPDA terminate in finite expected time?
Authors: Tobias Winkler, Joost-Pieter Katoen
Institution: RWTH Aachen University
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4384344688