Forming Sequences of Patterns With Luminous Robots

The extensive studies on computing by a team of identical mobile robots operating in the plane in Look-Compute-Move cycles have been carried out mainly in the traditional OBLOT model, where the robots are silent (have no communication capabilities) and oblivious (in a cycle, they have no memory previous cycles). To partially overcome the limits of obliviousness and silence while maintaining some of their advantages, the stronger model of luminous robots, LUMI, has been introduced where the robots, otherwise oblivious and silent, carry a visible light that can take a number of different colors; a color can be seen by observing robots, and persists from a cycle to the next. In the study of the computational impact of lights, an immediate concern has been to understand and determine the additional computational strength of LUMI over OBLOT. Within this line of investigation, we examine the problem of forming a sequence of geometric patterns, PatternSequenceFormation. A complete characterization of the sequences of patterns formable from a given starting configuration has been determined in the OBLOT model. In this paper, we study the formation of sequences of patterns in the LUMI model and provide a complete characterization. The characterization is constructive: our universal protocol forms all formable sequences, and it does so asynchronously and without rigidity. This characterization explicitly and clearly identifies the computational strength of LUMI over OBLOT with respect to the PatternSequenceFormation problem.