Asymptotic Complexity Estimates for Probabilistic Programs and their VASS Abstractions

TL;DR

This paper introduces new asymptotic complexity estimates for probabilistic programs with non-determinism, addressing limitations of traditional methods especially when expectations are infinite, and provides efficient analysis techniques for specific program classes.

Contribution

It proposes robust asymptotic estimates for probabilistic programs with non-determinism and demonstrates efficient analysis methods for Markov decision process representations.

Findings

New estimates handle infinite expectations effectively

Efficient analysis methods for vector addition system-based programs

Addresses robustness issues in traditional asymptotic complexity analysis

Abstract

The standard approach to analyzing the asymptotic complexity of probabilistic programs is based on studying the asymptotic growth of certain expected values (such as the expected termination time) for increasing input size. We argue that this approach is not sufficiently robust, especially in situations when the expectations are infinite. We propose new estimates for the asymptotic analysis of probabilistic programs with non-deterministic choice that overcome this deficiency. Furthermore, we show how to efficiently compute/analyze these estimates for selected classes of programs represented as Markov decision processes over vector addition systems with states.