Strategies in Sabotage Games: Temporal and Epistemic Perspectives

TL;DR

This paper analyzes sabotage games on dynamic graphs using temporal logic and epistemic extensions to understand winning strategies and address uncertainty.

Contribution

It introduces a temporal perspective with ATL* and explores epistemic aspects, advancing reasoning about strategies in sabotage games.

Findings

Framework supports reasoning about winning strategies.

Addresses players' uncertainty in epistemic extensions.

Opens new avenues for temporal analysis of dynamic graphs.

Abstract

Sabotage games are played on a dynamic graph, in which one agent, called a runner, attempts to reach a goal state, while being obstructed by a demon who at each round removes an edge from the graph. Sabotage modal logic was proposed to carry out reasoning about such games. Since its conception, it has undergone a thorough analysis (in terms of complexity, completeness, and various extensions) and has been applied to a variety of domains, e.g., to formal learning. In this paper, we propose examining the game from a temporal perspective using alternating time temporal logic (ATL$^\ast$), and address the players' uncertainty in its epistemic extensions. This framework supports reasoning about winning strategies for those games, and opens ways to address temporal properties of dynamic graphs in general.