We explore the computational power of formal models for computation
with pulses. Such models are motivated by realistic models for
biological neurons, and by related new types of VLSI (``pulse stream
VLSI'').

In preceding work it was shown that the computational power of formal
models for computation with pulses is quite high if the pulses
arriving at a computational unit have an approximately linearly rising
or linearly decreasing initial segment. This property is satisfied by
common models for biological neurons. On the other hand several
implementations of pulse stream VLSI employ pulses that are
approximately piecewise constant (i.e.~step functions).

In this article we investigate the relevance of the shape of pulses in
formal models for computation with pulses. It turns out that the
computational power drops significantly if one
replaces pulses with linearly rising or decreasing initial segments by
piecewise constant pulses. We provide an exact characterization of the
latter model in terms of a weak version of a random access machine
(RAM). We also compare the language recognition capability of a
recurrent version of this model with that of deterministic finite
automata and Turing machines.