  It is shown that for two large subclasses of discrete-time nonlinear systems
- analytic systems defined on a compact state space and rational systems - the
minimum length $r^*$ for input sequences, called here accessibility index of
the system, can be found, such that from any point $x$, system is accessible
iff it is accessible for input sequences of length $r^*$. Algorithms are
presented to compute $r^*$, as well as an upper bound for it, which can be
computed easier, and hence provide finite tests for determination of
accessibility. The algorithms also show how to construct the set of points from
which the system is not accessible in any finite number of steps. Finally, some
relations between generic accessibility of the system and accessibility of
individual points in finite steps are given.
