We consider several convergence problems for autonomous mobile robots under the $\cal SSYNC$ model. Let $\Phi$ and $\Pi $ be a set of target functions and a problem, respectively. If the robots whose target functions are chosen from $\Phi$ always solve $\Pi$, 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 $\Pi$. Note that even if both $\phi$ and $\phi'$ are algorithms for $\Pi$, $\{ \phi, \phi' \}$ may not be compatible with respect to $\Pi$. 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 problem, assuming crash failures. We classify these problems from the viewpoint of compatibility; the group of the convergence, FC(1), FC(1)-PO and FC($f$)-CP, and the group of the gathering and FC($f$)-PO for $f \geq 2$ have completely opposite properties. FC($f$) for $f \geq 2$ is placed in between.

翻译：我们考虑$\cal SSYNC$模型下自主移动机器人的若干收敛问题。设$\Phi$为目标函数集，$\Pi$为某个问题。若机器人的目标函数均选自$\Phi$时总能解决$\Pi$，则称$\Phi$关于$\Pi$兼容。当$\Phi$关于$\Pi\)兼容时，每个目标函数$\phi \in \Phi$均为$\Pi$的算法。注意即使$\phi$与$\phi'$均为$\Pi$的算法，$\{ \phi, \phi' \}$仍可能不关于$\Pi$兼容。我们研究崩溃故障假设下的收敛、容错$(n,f)$-收敛（FC($f$)）、容错$(n,f)$-收敛至$f$点（FC($f$)-PO）、容错$(n,f)$-收敛至凸$f$边形（FC($f$)-CP）以及聚集问题。我们从兼容性视角对这些问题进行归类：收敛、FC(1)、FC(1)-PO及FC($f$)-CP构成一组，而聚集与$f \geq 2$时的FC($f$)-PO具有完全相反的性质。$f \geq 2$时的FC($f$)则处于中间位置。