  The instantaneous state of a neural network consists of both the degree of
excitation of each neuron the network is composed of and positions of impulses
in communication lines between the neurons. In neurophysiological experiments,
the neuronal firing moments are registered, but not the state of communication
lines. But future spiking moments depend essentially on the past positions of
impulses in the lines. This suggests, that the sequence of intervals between
firing moments (inter-spike intervals, ISIs) in the network could be
non-Markovian.
  In this paper, we address this question for a simplest possible neural "net",
namely, a single inhibitory neuron with delayed feedback. The neuron receives
excitatory input from the driving Poisson stream and inhibitory impulses from
its own output through the feedback line. We obtain analytic expressions for
conditional probability density P(t_{n+1}| t_n,...,t_1,t_0), which gives the
probability to get an output ISI of duration t_{n+1} provided the previous
(n+1) output ISIs had durations t_n,...,t_1,t_0. It is proven exactly, that
P(t_{n+1}| t_n,...,t_1,t_0) does not reduce to P(t_{n+1}| t_n,...,t_1) for any
n>=0. This means that the output ISIs stream cannot be represented as a Markov
chain of any finite order.
