Summary form only given. A novel scheduling approach has been developed based on the deterministic Hopfield model for high-level synthesis. The model uses a four-dimensional neural network architecture to schedule the operations of a dataflow graph and maps them to specific functional units. Neural network-based scheduling is achieved by formulating the scheduling problem in terms of an energy function and by using the motion equation corresponding to the variation of energy. The algorithm searches the scheduling space in parallel and finds the optimal schedule. The main contribution of the present work is an efficient scheduling algorithm under time and resource constraints. The algorithm is based on moves in the scheduling space, which correspond to moves towards the equilibrium point (lowest energy state) in the dynamic system space. The neurons' motion equation is the heart of this guided movement mechanism and guarantees that the state of the system always converges to the lowest energy state.