Search NKS | Online
101 - 110 of 205 for Exists
Yet the fact that there are in the end regularities means that at least in principle there could exist higher forms of perception and analysis that would succeed in recognizing them.
And no doubt some other examples like this do exist.
And so what this means is that the problem of finding whether initial conditions exist that make the cellular automaton produce a certain outcome is equivalent to the non-deterministic Turing machine problem below—and is therefore in general NP-complete.
Such universality then implies Gödel's Theorem and shows that there must exist statements about arithmetic that cannot ever be proved true or false from its normal axioms.
Yet our experience has still been that to build a computer requires sophisticated engineering that in a sense exists only because of human biological and cultural development.
The substitution systems that we discussed in the previous section work by replacing each element in such a string by a new sequence of elements—so that in a sense these systems operate in parallel on all the elements that exist in the string at each step.
If the connections on the underlying network are one-way (as in causal networks) then one no longer necessarily gets the second property, and when a continuum limit exists it can correspond to a (perhaps discontinuous) section through a fiber bundle rather than to a manifold.
For I would have looked only for types of behavior that I already believed might exist.
Ever since machines have existed, people have wondered to what extent they might be able to imitate living systems.
So this suggests that a kind of universality exists in the types of behavior that can occur, independent of the details of underlying rules.