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This paper investigates a swarm of autonomous mobile robots in the Euclideanplane, under the semi-synchronous ($\cal SSYNC$) scheduler. Each robot has atarget function to determine a destination point from the robots' positions.All robots in the swarm take the same target function conventionally. We allowthe robots to take different target functions, and investigate the effects ofthe number of distinct target functions on the problem-solving ability,regarding target function as a resource to solve a problem like time.Specifically, we are interested in how many distinct target functions arenecessary and sufficient to solve a problem $\Pi$. The number of distincttarget functions necessary and sufficient to solve $\Pi$ is called the minimumalgorithm size (MAS) for $\Pi$. The MAS is defined to be $\infty$, if $\Pi$ isunsolvable even for the robots with unique target functions.  We show that the problems form an infinite hierarchy with respect to theirMASs; for each integer $c > 0$ and $\infty$, the set of problems whose MAS is$c$ is not empty, which implies that target function is a resourceirreplaceable, e.g., with time. We propose MAS as a natural measure to measurethe complexity of a problem.  We establish the MASs for solving the gathering and related problems from anyinitial configuration, i.e., in a self-stabilizing manner. For example, the MASfor the gathering problem is 2. It is 3, for the problem of gathering {\bf allnon-faulty} robots at a single point, regardless of the number $(< n)$ of crashfailures. It is however $\infty$, for the problem of gathering all robots at asingle point, in the presence of at most one crash failure.

Minimum algorithm sizes for self-stabilizing gathering and related problems of autonomous mobile robots