  We investigate autonomous mobile robots in the Euclidean plane. A robot has a
function called target function to decide the destination from the robots'
positions. Robots may have different target functions. If the robots whose
target functions are chosen from a set $\Phi$ of target functions always solve
a problem $\Pi$, we say that $\Phi$ is compatible with respect to $\Pi$. If
$\Phi$ is compatible with respect to $\Pi$, every target function $\phi \in
\Phi$ is an algorithm for $\Pi$. Even if both $\phi$ and $\phi'$ are algorithms
for $\Pi$, $\{ \phi, \phi' \}$ may not be compatible with respect to $\Pi$.
From the view point of compatibility, we investigate the convergence, the fault
tolerant ($n,f$)-convergence (FC($f$)), the fault tolerant ($n,f$)-convergence
to $f$ points (FC($f$)-PO), the fault tolerant ($n,f$)-convergence to a convex
$f$-gon (FC($f$)-CP), and the gathering problems, assuming crash failures.
Obtained results classify these problems into three groups: The convergence,
FC(1), FC(1)-PO, and FC($f$)-CP compose the first group: Every set of target
functions which always shrink the convex hull of a configuration is compatible.
The second group is composed of the gathering and FC($f$)-PO for $f \geq 2$: No
set of target functions which always shrink the convex hull of a configuration
is compatible. The third group, FC($f$) for $f \geq 2$, is placed in between.
Thus, FC(1) and FC(2), FC(1)-PO and FC(2)-PO, and FC(2) and FC(2)-PO are
respectively in different groups, despite that FC(1) and FC(1)-PO are in the
first group.
