British Computer Society (BCS)

What is the universal nilpotent computational rewrite system?

See arXiv.cs.OH/0209026 and IJCAS Proceedings of CASYS’03, vol.16, 2004, 203-218
A Computational Path to the Nilpotent Dirac Equation
Diaz B.M. & Rowlands for further details
It differs from traditional rewrite systems (of computational semantic language description with a fixed or finite alphabet) in that the rewrite rules allow new symbols to be added to the initial alphabet. In fact D&R start with just one symbol representing "nothing" and two fundamental rules; create a process which adds new symbols and conserve a process that examines the effect of any new symbol on those that currently exist to ensure “a zero sum” again. In this way at each step a new sub-alphabet of an infinite universal alphabet is created. However the system may also be implemented in an iterative way, so that a sequence of mathematical properties is required of the emerging sub-alphabets. D&R show that one such sequential iterative path proceeds from nothing (corresponding to the mathematical condition nilpotent) through conjugation, complexification, and dimensionalization to a stage in which no fundamentally new symbol is needed. At this point the alphabet is congruent with the nilpotent generalization of Dirac’s famous quantum mechanical equation showing that it defines the quantum mechanical “machine order code” for all further (universal) computation corresponding to the infinite universal alphabet⁺⁺. This rewrite system with its nilpotent bootstrap methodology (Page 3) from “nothing/the empty set” thus defines the requirement for universal quantum computation to constitute a semantic model of computation with a universal grammar.

⁺⁺since a new symbol can stand for itself, a sub-alphabet or the infinite universal alphabet, the universal nilpotent rewrite system may thus rewrite itself, ontologically at a higher (hierarchical) level of quantum physical structure.