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State-based sequence processors
Sequence processors may be built around a state; state-based
sequence
processors maintain and update at each time
a state
which stores the information about the input sequence they have
seen so far (
) which is necessary to compute the
current output
or future outputs. State is recursively
computed: the state at time
,
, is computed from the state at
time
,
, and the current input
using a suitable
next-state function:
![\begin{displaymath}
x[t]=f(x[t-1],u[t]).
\end{displaymath}](img116.png) |
(4.1) |
The output is then computed using an output function, usually
from the current state,
![\begin{displaymath}
y[t]=h(x[t]),
\end{displaymath}](img117.png) |
(4.2) |
but sometimes from the previous state and the current input, like
current state itself
![\begin{displaymath}
y[t]=h(x[t-1],u[t]).
\end{displaymath}](img118.png) |
(4.3) |
Such a state-based sequence processor is therefore defined by the set
of available states, by its initial state
, and by the
next-state (
) and output (
) functions (the nature of
inputs and outputs is defined by the task itself). For example, Mealy
and Moore machines (sections 2.3.1 and 2.3.2) and
deterministic finite-state automata (section 2.3.3) are
sequence processors having a finite set of available states. As will
be seen in the following section, neural networks may be used and
trained as state-based adaptive sequence processors.
.
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Debian User
2002-01-21