1. A computer-implemented process for examining concurrent system state space, the computer-implemented process comprising: modeling a system having concurrent events to create a modeled system; creating a minimal chain decomposition of the modeled system to identify a set of chains; extending all chains in the set of chains, wherein all the chains include a plurality of chains and wherein extending all chains in the set of chains comprises: creating a path for each chain, from a bottom to a smallest element s of a chain by adding to an empty set all events that are part of s, one event at the time, in any order; and creating a path from a largest element l of a chain to a top by adding to l all events that are missing from a largest element, one event at the time, in any order; generating a first set of paths, wherein the first set of paths is a minimal set of paths covering all states of the modeled system; and exploring the first set of paths.