2025/04/22 by Lemke, Caroline, Benjamin Bisping, Bisping, Benjamin
Computer Science · #Semantic Web and Ontologies #Advanced Database Systems and Queries #Graph Theory and Algorithms
paper · pdf · doi:10.48550/arxiv.2505.14691
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.