# Spiking Neurons and the Induction of Finite State Machines

**T. Natschlaeger and W. Maass**

### Abstract:

We discuss in this short survey article some current mathematical models from
neurophysiology for the computational units of biological neural systems:
neurons and synapses. These models are contrasted with the computational
units of common artificial neural network models, which reflect the state of
knowledge in neurophysiology 50 years ago. We discuss the problem of carrying
out computations in circuits consisting of biologically realistic
computational units, focusing on the biologically particularly relevant case
of computations on time series. Finite state machines are frequently used in
computer science as models for computations on time series. One may argue
that these models provide a reasonable common conceptual basis for analyzing
computations in computers and biological neural systems, although the
emphasis in biological neural systems is shifted more towards asynchronous
computation on analog time series. In the second half of this article some
new computer experiments and theoretical results are discussed, which address
the question whether a biological neural system can in principle learn to
behave like a given simple finite state machine.

**Reference:** T. Natschlaeger and W. Maass.
Spiking neurons and the induction of finite state machines.
*Theoretical Computer Science: Special Issue on Natural Computing*,
287:251-265, 2002.