  Fredkin's Billiard Ball Model (BBM) is considered one of the fundamental
models of collision-based computing, and it is essentially based on elastic
collisions of mobile billiard balls. Moreover, fixed mirrors or reflectors are
brought into the model to deflect balls to complete the computation. However,
the use of fixed mirrors is "physically unrealistic" and makes the BBM not
perfectly momentum conserving from a physical point of view, and it imposes an
external architecture onto the computing substrate which is not consistent with
the concept of "architectureless" in collision-based computing. 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 collision-based computing in novel chemical and optical computing
substrates.
