In this paper, we propose decentralized control of networks of discrete-time nonlinear control systems, enforcing complex specifications expressed in terms of regular languages, within any desired accuracy. As discussed in the paper, regular languages are useful to model a rather wide variety of complex specifications for control systems. The design of decentralized controllers is based on formal methods and, in particular, on the use of discrete abstractions. Efficient synthesis of such controllers is derived by resorting to on-the-fly algorithmic techniques that also allow the use of parallel computing architectures. Advantages and disadvantages of the decentralized approach over a centralized one, also in terms of computational complexity, are discussed. An illustrative example is presented, which shows the applicability and effectiveness of the results proposed.