Abstract: A method for analyzing reachability of a Petri net and deriving the control-related state of the PN extended from the kth variant closed-form formula (CFF) system for numbers, comprising by proving that the first system Gen-Right(k, gen) and the second system Gen_Left(k, k?gen) are topological inverse networks of Gen-Left(k, gen), the first system and the second system An invertible one-to-one mapping between; wherein the first series Gen-Right(k, gen) and Gen-Left(k, k?gen) have the same closed-form formula, and by putting Gen-Left(k, gen) in the verified closed-form formula The parameter gen can be obtained by replacing it with k?gen, and its corresponding reachability state can be directly obtained through a reversible one-to-one mapping.