The neurally inspired accumulative computation (AC) method and its application to motion detection have been introduced in the past years. This paper revisits the fact that many researchers have explored the relationship between neural networks and finite state machines. Indeed, finite state machines constitute the best characterized computational model, whereas artificial neural networks have become a very successful tool for modeling and problem solving. The article shows how to reach real-time performance after using a model described as a finite state machine. This paper introduces two steps towards that direction: (a) A simplification of the general AC method is performed by formally transforming it into a finite state machine. (b) A hardware implementation in FPGA of such a designed AC module, as well as an 8-AC motion detector, providing promising performance results. We also offer two case studies of the use of AC motion detectors in surveillance applications, namely infrared-based people segmentation and color-based people tracking, respectively.