Concurrent Permissive Strategy Templates

Two-player games on finite graphs provide a rigorous foundation for modeling the strategic interaction between reactive systems and their environment. While concurrent game semantics naturally capture the synchronous interactions characteristic of many cyber-physical systems (CPS), their adoption in CPS design remains limited. Building on the concept of permissive strategy templates (PeSTels) for turn-based games, we introduce concurrent (permissive) strategy templates (ConSTels) – a novel representation for sets of randomized winning strategies in concurrent games with Safety, Büchi, and Co-Büchi objectives. ConSTels compactly encode infinite families of strategies, thereby supporting both offline and online adaptation. Offline, we exploit compositionality to enable incremental synthesis: combining ConSTels for simpler objectives into non-conflicting templates for more complex combined objectives. Online, we demonstrate how ConSTels facilitate runtime adaptation, adjusting action probabilities in response to observed opponent behavior to optimize performance while preserving correctness. We implemented ConSTel synthesis and adaptation in a prototype tool and experimentally show its potential.