2017/06/16 by Arnaud Sangnier, Nathalie Sznajder, Sangnier, Arnaud +5
Computer Science · #Computational Complexity (cs.CC) #Data Structures and Algorithms (cs.DS) #Distributed #Distributed systems and fault tolerance #FOS: Computer and information sciences #Formal Methods in Verification #Logic in Computer Science (cs.LO) #Optimization and Search Problems #Parallel #Robotics (cs.RO) #and Cluster Computing (cs.DC) #cs.CC #cs.DC #cs.DS #cs.LO #cs.RO
paper · pdf · doi:10.48550/arxiv.1706.05193
arxiv created 2017/06/16 · openalex publication_date 2017/06/16 · arxiv updated 2017/06/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study verification problems for autonomous swarms of mobile robots that self-organize and cooperate to solve global objectives. In particular, we focus in this paper on the model proposed by Suzuki and Yamashita of anonymous robots evolving in a discrete space with a finite number of locations (here, a ring). A large number of algorithms have been proposed working for rings whose size is not a priori fixed and can be hence considered as a parameter. Handmade correctness proofs of these algorithms have been shown to be error-prone, and recent attention had been given to the application of formal methods to automatically prove those. Our work is the first to study the verification problem of such algorithms in the parameter-ized case. We show that safety and reachability problems are undecidable for robots evolving asynchronously. On the positive side, we show that safety properties are decidable in the synchronous case, as well as in the asynchronous case for a particular class of algorithms. Several properties on the protocol can be decided as well. Decision procedures rely on an encoding in Presburger arithmetics formulae that can be verified by an SMT-solver. Feasibility of our approach is demonstrated by the encoding of several case studies.