Stochastic Parity Games on Lossy Channel Systems

TL;DR

This paper presents an algorithm for solving stochastic parity games with almost-sure winning conditions on lossy channel systems, focusing on finite-memory strategies and utilizing a finite attractor framework.

Contribution

It introduces a general framework for 2 1/2-player games with almost-sure parity conditions on infinite graphs, and applies it to develop an algorithm for stochastic game lossy channel systems.

Findings

Algorithm for stochastic parity games on lossy channel systems.

Framework based on finite attractors for infinite game graphs.

Applicable to finite-memory strategies in probabilistic settings.

Abstract

We give an algorithm for solving stochastic parity games with almost-sure winning conditions on {\it lossy channel systems}, under the constraint that both players are restricted to finite-memory strategies. First, we describe a general framework, where we consider the class of 2 1/2-player games with almost-sure parity winning conditions on possibly infinite game graphs, assuming that the game contains a {\it finite attractor}. An attractor is a set of states (not necessarily absorbing) that is almost surely re-visited regardless of the players' decisions. We present a scheme that characterizes the set of winning states for each player. Then, we instantiate this scheme to obtain an algorithm for {\it stochastic game lossy channel systems}.