Liang ZHANG
Abstract. In collision-based computing, wires and gates are dynamically constructed by traveling localizations in spatially-extended architectureless medium and the computation is performed by their mutual collisions. One of the pioneer models of collision-based computing is Fredkin's Billiard Ball Model (BBM), which is essentially based on elastic collisions of mobile billiard balls. However, the use of mirrors imposes external architecture to the model. Also, fixed mirrors are physically unrealistic and make the BBM not perfectly momentum conserving. In our initial attempt to reduce mirrors in the BBM, we present a class of gates: the m-counting gate, and show that certain circuits can be realized with few mirrors using this gate. We envisage that our findings can be useful in future research of collsion-based computing in novel computing substrates.