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Universality is the property of being able to perform different tasks with the same underlying construction just by being programmed in a different way. Universal systems are ...

A multiway system that generates causal networks which are all isomorphic as acyclic digraphs is said to exhibit causal invariance, and the causal network itself is also said ...

A causal network is an acyclic digraph arising from an evolution of a substitution system, and representing its history. The illustration above shows a causal network ...

A function H that maps an arbitrary length message M to a fixed length message digest MD is a collision-free hash function if 1. It is a one-way hash function. 2. It is hard ...

A number which can be computed to any number of digits desired by a Turing machine. Surprisingly, most irrationals are not computable numbers!

Some computations allow shortcuts which can be used to speed them up. Consider the operation of raising a number to a positive integer power. It is possible, for example, to ...

An encoding is a way of representing a number or expression in terms of another (usually simpler) one. However, multiple expressions can also be encoded as a single ...

There are two camps of thought on the meaning of general recursive function. One camp considers general recursive functions to be equivalent to the usual recursive functions. ...

An iterated map is a map that is applied repeatedly to an object. The Wolfram Language function NestList[f, expr, n] gives a list of the results of iterating the function f n ...

A nondeterministic Turing machine is a "parallel" Turing machine that can take many computational paths simultaneously, with the restriction that the parallel Turing machines ...