Sparse Positional Strategies for Safety Games
R\"udiger Ehlers (Saarland University), Daniela Moldovan (Saarland, University)

TL;DR
This paper compares various methods, including ILP, SAT, and iterative linear programming, for generating sparse positional strategies in safety games, which are crucial in formal methods for creating compact certificates of winning strategies.
Contribution
It provides a comparative analysis of existing techniques for producing sparse strategies in safety games, introducing a novel iterative linear programming approach.
Findings
ILP and SAT methods are effective but may lack scalability.
The iterative linear programming technique shows promising results.
Current methods' scalability needs improvement for practical applications.
Abstract
We consider the problem of obtaining sparse positional strategies for safety games. Such games are a commonly used model in many formal methods, as they make the interaction of a system with its environment explicit. Often, a winning strategy for one of the players is used as a certificate or as an artefact for further processing in the application. Small such certificates, i.e., strategies that can be written down very compactly, are typically preferred. For safety games, we only need to consider positional strategies. These map game positions of a player onto a move that is to be taken by the player whenever the play enters that position. For representing positional strategies compactly, a common goal is to minimize the number of positions for which a winning player's move needs to be defined such that the game is still won by the same player, without visiting a position with an…
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