Search NKS | Online
81 - 90 of 205 for Exists
Both the examples on this page show structures that exist on very regular backgrounds.
But the fact that no short description can be found by our usual processes of perception and analysis does not in any sense mean that no such description exists at all.
To get a spectrum with a more elaborate structure requires long-range correlations—as exist in nested sequences.
And what this suggests is that a fundamental unity exists across a vast range of processes in nature and elsewhere: despite all their detailed differences every process can be viewed as corresponding to a computation that is ultimately equivalent in its sophistication.
But I strongly suspect that even though it may be quite impractical to find particular computations that one wants, it is still the case that essentially any possible computation exists somewhere in the pattern.
And when I first started looking at systems like cellular automata I in effect implicitly assumed that some such form of regularity must exist.
For the principle asserts that the same computational equivalence exists for absolutely any method of perception and analysis that can actually be used.
any proof—regardless of length—exists for a specific result in a mathematical system with particular axioms.
At each step, the rule then specifies that the string which exists at that step should be scanned from left to right, and the first sequence BA that is found should be replaced by ABA .
A formula of polynomial size and logarithmic depth exists only when a function is the computational complexity class NC discussed on page 1149 .