About the Universality of the Billiard ball model

Block cellular automata (BCA) make local, parallel, synchronous and uniform updates of in nite lattices. In the one-dimensionalcase, there exist BCA with 11 states which are universal for computation. The Billiardballmodelof Margolusis a reversible two-dimensionalBCA which is able to simulateany two-register automatonand is thus universal. This simulationis achieved by embedding a logicalcircuitry with balls. The construction uses Fredkin gate and conservative and reversible logics.

• Type: Conference
• Year: 1998
• Where: MCU
• Authors: Jérôme Olivier Durand-Lose
• Keywords: Block Cellular Automata, MCU 1998, MCU 2007, Nite Lattices, Uniform Updates