Establishing the NP-hardness of maximally permissive RAS-based approaches to multi-vehicle system safety

The safety problem in multi-vehicle systems seeks to establish collision-free and live vehicle motion, and it is a prominent problem for many configurations of these environments. Past work studying this problem in the context of free-range vehicular systems through abstractions based on Resource Allocation System (RAS) theory, has implicitly assumed that its resolution through maximally permissive supervision is NP-hard, and therefore, it has typically pursued suboptimal (i.e., more restrictive) solutions. The work presented in this paper offers formal proof to this implicit assumption, closing the apparent gap in the existing literature.