Research Vision: Multi-Agent Path Planning for Cops And Robbers Via Reactive Synthesis
William Fishell, Andoni Rodriguez, Mark Santolucito
TL;DR
This work reframes the classic Cops and Robbers game as a multi-agent reactive-synthesis problem, using LTL$t$ and Coordination Synthesis to decide realizability and to generate executable strategies for cop and robber agents. It systematically extends the traditional game to (i) robbers as system players and (ii) cops as system players, across perfect and imperfect information, finite and infinite grids, and with safe zones and memory-sharing capabilities. The approach proposes expressing complex, theory-rich environmental dynamics with LTL$t$ and abstracting via Boolean representations to enable scalable synthesis, while positioning the framework to map onto broader domains such as multi-agent path planning and logistics. The envisioned contributions include a formal problem formalization, a spectrum of game variants, and an outline of a solving strategy that yields a coordinator/controller capable of correct-by-construction policy extraction for each agent, with potential applicability to reinforcement learning hybrids and related graph problems.
Abstract
We propose the problem of multi-agent path planning for a generalization of the classic Cops and Robbers game via reactive synthesis. Specifically, through the application of LTLt and Coordination Synthesis, we aim to check whether various Cops and Robbers games are realizable (a strategy exists for the cops which guarantees they catch the robbers). Additionally, we construct this strategy as an executable program for the multiple system players in our games. In this paper we formalize the problem space, and propose potential directions for solutions. We also show how our formalization of this generalized cops and robbers game can be mapped to a broad range of other problems in the reactive program synthesis space.