A computer-implemented process, computer program product, and apparatus for examining concurrent system state space models. A system has concurrent events to create a modeled system. A minimal chain decomposition of the modeled system is created to identify a set of chains. All chains in the set of chains are extended, and a first set of paths is generated, wherein the first set of paths is a minimal set of paths covering all states of the modeled system. The first set of paths is explored. It is optionally determined whether all transitions have been covered. Responsive to a determination that all transitions have not been covered, remaining paths are explored by traversing a graph induced by the modeled system using a depth-first strategy.