Reachability Switching Games

TL;DR

This paper analyzes the computational complexity of reachability switching games across different player scenarios, revealing that these deterministic games are generally harder than their stochastic counterparts.

Contribution

It establishes complexity bounds for zero-, one-, and two-player reachability switching games, including hardness and membership results in various models.

Findings

Zero-player case is NL-hard.

One-player case is NP-complete.

Two-player case is PSPACE-hard and in EXPTIME.

Abstract

We study the problem of deciding the winner of reachability switching games for zero-, one-, and two-player variants. Switching games provide a deterministic analogue of stochastic games. We show that the zero-player case is NL-hard, the one-player case is NP-complete, and that the two-player case is PSPACE-hard and in EXPTIME. For the zero-player case, we also show P-hardness for a succinctly-represented model that maintains the upper bound of NP $\cap$ coNP. For the one- and two-player cases, our results hold in both the natural, explicit model and succinctly-represented model. Our results show that the switching variant of a game is harder in complexity-theoretic terms than the corresponding stochastic version.