Automated Approach for Solving Infinite-state Polynomial Reachability Games

Researchers have developed a novel automated method for solving infinite-state polynomial reachability games, a critical area in artificial intelligence and reactive synthesis. The study addresses turn-based games on infinite-state graphs defined by real variable valuations, focusing on computing winning strategies for the REACH player. The team introduces ranking certificates, a sound and complete proof rule verifying winning strategies from initial states. Furthermore, they propose a fully automated algorithm for polynomial reachability games, where transitions and objectives are governed by polynomial constraints. This algorithm is sound, semi-complete, and operates in sub-exponential time, providing formal correctness witnesses via ranking certificates. Experimental results demonstrate the method's superiority over existing techniques, successfully solving complex literature examples previously deemed intractable. Notably, the approach computes an optimal winning strategy for the classical Cinderella-Stepmother game with arbitrary precision for the first time. This advancement significantly enhances the capability to handle challenging infinite-state systems in AI applications.