-- Collective decision-making is a key function of autonomous robot swarms, enabling them to reach a consensus on actions based on environmental features. Existing strategies require the participation of all robots in the decision-making process, which is resource-intensive and prevents the swarm from allocating the robots to any other tasks. We propose Subset-Based Collective Decision-Making (SubCDM), which enables decisions using only a swarm subset. The construction of the subset is dynamic and decentralized, relying solely on local information. Our method allows the swarm to adaptively determine the size of the subset for accurate decision-making, depending on the difficulty of reaching a consensus. Simulation results using one hundred robots show that our approach achieves accuracy comparable to using the entire swarm while reducing the number of robots required to perform collective decision-making, making it a resource-efficient solution for collective decision-making in swarm robotics. Swarm robotics is a rapidly growing area of research, gaining significant attention due to its broad potential applications across various fields [1].

We present a novel perspective on the NFA canonization problem, which introduces intermediate minimization steps to reduce the exploration space on-the-fly. Essential to our approach are so-called equivalence registries which manage information about equivalent states and allow for incorporating further optimization techniques such as convexity closures or simulation to boost performance. Due to the generality of our approach, these concepts can be embedded in classic subset construction or Brzozowski's approach. We evaluate our approach on a set of real-world examples from automatic sequences and observe that we are able to improve especially worst-case scenarios. We implement our approach in an open-source library for users to experiment with.