Circle formation of weak robots and Lyndon words

Lyndon words, which are used to build and to prove an efficient and simple deterministic protocol solving the CFP for a prime number of robots greater than or equal to 5 and their applications are discussed. Lyndon words can be used in the distributed control of a set of n anonymous robots being memoryless, without any common sense of direction, and unable to communicate in an other way than observation. An efficient and simple deterministic protocol to form a regular n-gon was presented for a prime number of robots. Lyndon words has proven itself efficient in solving the Circle Formation Problem without any arbitrary number of robots.