We provide a generic decision procedure for energy games with energy-bounded attacker and reachability objective, moving beyond vector-valued energies and vector-addition updates. All we demand is that energies form well-founded bounded join-semilattices, and that energy updates have an upward-closed domain and can be "undone" through a Galois-connected function. We instantiate these Galois energy games to common energy games, declining energy games, multi-weighted reachability games, coverability on vector addition systems with states and shortest path problems, supported by an Isabelle-formalization and two implementations. For these instantiations, our simple algorithm is polynomial w.r.t. game graph size and exponential w.r.t. dimension.
@article{arxiv.2505.14691,
title = {Galois Energy Games: To Solve All Kinds of Quantitative Reachability Problems},
author = {Caroline Lemke and Benjamin Bisping},
journal= {arXiv preprint arXiv:2505.14691},
year = {2025}
}