Notes on spiking neural P systems and finite automata

Spiking neural P systems (in short, SN P systems) are membrane computing models inspired by the pulse coding of information in biological neurons. SN P systems with standard rules have neurons that emit at most one spike (the pulse) each step, and have either an input or output neuron connected to the environment. A variant known as SN P modules generalize SN P systems by using extended rules (more than one spike can be emitted each step) and a set of input and output neurons. In this work we continue relating SN P modules and finite automata. In particular, we amend and improve previous constructions for the simulatons of deterministic finite automata and state transducers. Our improvements reduce the number of neurons from three down to one, so our results are optimal. We also simulate finite automata with output, and we use these simulations to generate automatic sequences.