标题： 在台球模型中自然计算 显示英文标题

标题： Computing Naturally in the Billiard Ball Model

摘要： 弗雷德金弹珠模型（BBM）被认为是基于碰撞计算的基本模型之一，其本质上基于移动弹珠的弹性碰撞。 此外，固定镜面或反射器被引入该模型以偏转弹珠完成计算。 然而，使用固定镜面在物理上是“不现实的”，从物理角度来看，这使得BBM不能完全保持动量守恒，并且在计算基质上强加了一个外部架构，这与基于碰撞计算中的“无架构”概念不一致。 在我们最初尝试减少BBM中镜面的尝试中，我们提出了一类门：m计数门，并表明某些电路可以使用此门用少量镜面实现。 我们设想，我们的发现可能在新型化学和光学计算基质中的基于碰撞计算的未来研究中有用。 显示英文摘要

摘要： 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.