A reduction from parity games to simple stochastic games

TL;DR

This paper introduces a straightforward and efficient reduction from deterministic parity games to simple stochastic games, enabling easier analysis of complex reactive systems modeled by these graph-based games.

Contribution

It provides the first linear (up to a logarithmic factor) reduction from parity games to simple stochastic games, simplifying their analysis.

Findings

Reduction has linear size up to a logarithmic factor

Enables easier analysis of parity games via stochastic game techniques

Improves understanding of the relationship between different game types

Abstract

Games on graphs provide a natural model for reactive non-terminating systems. In such games, the interaction of two players on an arena results in an infinite path that describes a run of the system. Different settings are used to model various open systems in computer science, as for instance turn-based or concurrent moves, and deterministic or stochastic transitions. In this paper, we are interested in turn-based games, and specifically in deterministic parity games and stochastic reachability games (also known as simple stochastic games). We present a simple, direct and efficient reduction from deterministic parity games to simple stochastic games: it yields an arena whose size is linear up to a logarithmic factor in size of the original arena.