Exploring Millions of 6-State FSSP Solutions: the Formal Notion of Local CA Simulation

In this paper, we come back on the notion of local simulation allowing to transform a cellular automaton into a closely related one with different local encoding of information. This notion is used to explore solutions of the Firing Squad Synchronization Problem that are minimal both in time (2n -- 2 for n cells) and, up to current knowledge, also in states (6 states). While only one such solution was proposed by Mazoyer since 1987, 718 new solutions have been generated by Clergue, Verel and Formenti in 2018 with a cluster of machines. We show here that, starting from existing solutions, it is possible to generate millions of such solutions using local simulations using a single common personal computer

Social Graphs and Their Applications to Robotics

In this thesis, we propose a new method to design a roadmap-based path planning algorithm in a 2D static environment, which assumes a-priori knowledge of robots’ positions, their goals’ positions, and surrounding obstacles. The new algorithm, called Multi-Robot Path Planning Algorithm (MRPPA), combines Visibility graph VG method with the algebraic connectivity