arXiv:1101.2002v3 [cs.SY] 17 Aug 2012 Technical Report: NUS-ACT-12-001-Ver.3: Cooperative Tasking for Deterministic Speciﬁcation Automata Preprint, Submitted for publication Mohammad Karimadini, and Hai Lin, Abstract In our previous work [1], a divide-and-conquer approach was proposed for cooperative tasking among multi-agent systems. The basic idea is to decompose a requested global speciﬁcation into subtasks for individual agents such that the fulﬁllment of these subtasks by each individual agent leads to the satisfaction of the global speciﬁcation as a team. It was shown that not all tasks can be decomposed. Furthermore, a necessary and sufﬁcient condition was proposed for the decomposability of a task automaton between two cooperative agents. The current paper continues the results in [1] and proposes necessary and sufﬁcient conditions for task decomposability with respect to arbitrary ﬁnite number of agents. It is further shown that the fulﬁllment of local speciﬁcations can guarantee the satisfaction of the global speciﬁcation. This work provides hints for the designers on how to rule out the indecomposable task automata and enforce the decomposability conditions. The result therefore may pave the way towards a new perspective for decentralized cooperative control of multi-agent systems. I. INTRODUCTION Multi-agent system emerges as a rapidly developing multi-disciplinary area with promis- ing applications in assembling and transportation, parallel computing, distributed planning and scheduling, rapid emergency response and multi-robot systems [2], [3], [4], [5]. The signiﬁcance M. Karimadini is with the Department of Electrical and Computer Engineering, National University of Singapore, Singapore. H. Lin is from the Department of Electrical Engineering University of Notre Dame, IN 46556 USA. Corresponding author, H. Lin {hlin1@nd.edu}.