Computational Power of Mobile Robots in Synchronous Environment: Discrete Version (2407.05678v4)

Abstract: In distributed computing by mobile robots, robots are deployed over a region, continuous or discrete, operating through a sequence of \textit{look-compute-move} cycles. An extensive study has been carried out to understand the computational powers of different robot models. The models vary on the ability to 1)~remember constant size information and 2)~communicate constant size message. Depending on the abilities the different models are 1)~$\mathcal{OBLOT}$ (robots are oblivious and silent), 2)~$\mathcal{FSTA}$ (robots have finite states but silent), 3)~$\mathcal{FCOM}$ (robots are oblivious but can communicate constant size information) and, 4)~$\mathcal{LUMI}$ (robots have finite states and can communicate constant size information). Another factor that affects computational ability is the scheduler that decides the activation time of the robots. The main three schedulers are \textit{fully-synchronous}, \textit{semi-synchronous} and \textit{asynchronous}. Combining the models ($M$) with schedulers ($K$), we have twelve combinations $M^K$. In the euclidean domain, the comparisons between these twelve variants have been done in different works for transparent robots, opaque robots, and robots with limited visibility. There is a vacant space for similar works when robots are operating on discrete regions like networks. It demands separate research attention because there have been a series of works where robots operate on different networks, and there is a fundamental difference when robots are operating on a continuous domain versus a discrete domain in terms of robots' movement. This work contributes to filling the space by giving a full comparison table for all models with two synchronous schedulers: fully-synchronous and semi-synchronous.