Asynchronous programs utilize asynchronous non-blocking calls to achieve program concurrency, and they are widely applied in parallel and distributed systems. However, it is very complex to verify asynchronous programs, and the difficulty can be ranked as EXPSPACE in terms of both safety and liveness. This study proposes a program model of asynchronous programs and defines two problems of asynchronous programs, namely, ?-equivalence and ?-reachability. In addition, the two problems can be proved to be NP-complete by reducing the 3-CNF-SAT to the problems and making them further reduced to the reachability of the communication-free Petri net. The case shows that the two problems can solve the verification problems of asynchronous programs.