Decomposability of global tasks for multi-agent systems

Multi-agent system is a rapidly developing research area with strong support from both civilian and military applications. One of the essential problems in multi-agent system research is how to design local interaction rules and coordination principles among agents such that the whole system achieves desired global behaviors. To tackle this problem, a divide-and-conquer approach was proposed in, and the basic idea is to decompose the requested global specification into subtasks for individual agents in such a way that the fulfillment of these subtasks by each individual agent should lead to the satisfaction of the global specification. Then, the design reduces to achieving the assigned subtasks for corresponding individual agents. In, it was shown that not all global tasks can be decomposed, and a necessary and sufficient condition on the decomposability of a task automaton between two agents was presented. For more than two agents, we then proposed a hierarchical algorithm as a sufficient condition for decomposability. This paper aims to extend the necessary and sufficient decomposability conditions for any arbitrary finite number of cooperative agents. A new necessary and sufficient condition on decomposability of a task automaton is proposed, here. Several examples are provided to illustrate the decomposition scheme and conditions.