Traversability, Reconfiguration, and Reachability in the Gadget Framework

Abstract Consider an agent traversing a graph of “gadgets”, where each gadget has local state that changes with traversal by the according to specified rules. Prior work studied computational complexity deciding whether can reach location, problem we call reachability . This paper introduces new goals for agent, aiming characterize when these problems is same or differs from reachability. First universal —where goal traverse every at least once—for DAG gadgets (partially), one-state gadgets, and reversible deterministic gadgets. Then study reconfiguration bring system state. We prove many cases PSPACE-complete, show in some strictly harder than reachability, while other cases, reconfiguration.