We study the computational power that oblivious robots operating in the plane have under sequential schedulers. We show that this power is much stronger than the obvious capacity these schedulers offer of breaking symmetry, and thus to create a leader. In fact, we prove that under any sequential scheduler, robots are capable of solving problems that are unsolvable even with a leader under the fully synchronous scheduler FSYNC. More precisely, we consider the class of pattern formation problems, and focus on the most general problem in this class, Universal Pattern Formation (UPF), which requires the robots to form every pattern given in input, starting from any initial configuration (where some robots may occupy the same point, hence forming a multiplicity). We first show that UPF is unsolvable under FSYNC, even if the robots are endowed with additional strong capabilities (multiplicity detection, rigid movement, agreement on coordinate systems, presence of a unique leader). On the other hand, we prove that, except for point formation (Gathering), UPF is solvable under any sequential scheduler without any additional assumptions. We then turn our attention to the Gathering problem, and prove that weak multiplicity detection (the ability to detect a multiplicity but not the exact number of robots forming it) is necessary and sufficient for solvability under sequential schedulers. The results obtained show that the computational power of the robots under FSYNC (where Gathering is solvable without any multiplicity detection) and that under sequential schedulers are orthogonal.

翻译：我们研究了在平面上运行的无记忆机器人在顺序调度器下的计算能力。研究表明，这种能力远强于这些调度器所提供的打破对称性（从而创建领导者）的明显能力。事实上，我们证明在任何顺序调度器下，机器人能够解决即使在完全同步调度器FSYNC下拥有领导者也无法解决的问题。更具体地说，我们考虑模式形成问题类，并聚焦于该类中最一般的问题——通用模式形成（UPF），该问题要求机器人从任意初始配置（其中某些机器人可能占据同一点，从而形成多重性）出发，形成所有给定的输入模式。我们首先证明，即使在机器人具备额外强大能力（多重性检测、刚性移动、坐标系一致性、存在唯一领导者）的情况下，UPF在FSYNC下也是不可解的。另一方面，我们证明除了点形成（聚集）问题外，UPF在任何顺序调度器下无需任何额外假设即可求解。随后我们将注意力转向聚集问题，并证明弱多重性检测（能够检测多重性但无法精确识别构成该多重性的机器人数量）对于顺序调度器下的可解性是必要且充分的。所得结果表明，机器人在FSYNC下的计算能力（其中聚集问题无需任何多重性检测即可求解）与在顺序调度器下的计算能力具有正交性。