Narrow Results

This paper explains the important conceptual and technical differences between the method of p-cycles and two other recent advances involving a cyclic orientation to protection. These are enhanced rings and cycle double covers. The most fundamental difference that is unique to p-cycles is the aspect of straddling span failure protection. This enables mesh-like efficiency levels at well under 100% redundancy. In contrast enhanced rings and advanced cycle cover methods are both seeking to reduce span overlaps in what is otherwise a purely ring-like logical paradigm in which 100% redundancy remains the best that can possibly be achieved.

In this paper, we will review the developing features of computations based on rings. Particularly, we will analyse what kinds of interaction occur between gliders travelling on a ‘cyclotron’ cellular automaton derived from a catalog of collisions. We will demonstrate that collisions between gliders emulate the basic types of interaction that occur between localizations in non-linear media: fusion, elastic collision, and soliton-like collision. Computational outcomes of a swarm of gliders circling on a one-dimensional torus are analysed via implementation of some simple computing models. Gliders in one-dimensional cellular automata are compact groups of non-quiescent patterns translating along an automaton lattice. They are cellular-automaton analogous to localizations or quasi-local collective excitations travelling in a spatially extended non-linear medium. So, they can be represented as binary strings or symbols travelling along a one-dimensional ring, interacting with each other and changing their states, or symbolic values, as a result of interactions. We present a number of complex one-dimensional cellular automata with such features.