Abstract: A neural network simulation represents components of neurons by finite state machines, called sectors, implemented using look-up tables. Each sector has an internal state represented by a compressed history of data input to the sector and is factorized into distinct historical time intervals of the data input. The compressed history of data input to the sector may be computed by compressing the data input to the sector during a time interval, storing the compressed history of data input to the sector in memory, and computing from the stored compressed history of data input to the sector the data output from the sector.