(Ordinary primitive recursive functions are always total functions, that give definite values for every possible input. But general recursive functions can be partial functions, that do not terminate for some inputs.) … (Note that any general recursive function can be expressed in the form c[f, μ [g]] where f and g are primitive recursive.)

The input comes from the left encoded as the presence or absence of spaceships 92 cells apart. … But when two gliders are present, their collision forms a wall, which prevents output of the spaceship.

In the early 1900s devices based on randomness were built to illustrate statistics and probability (see page 312 ), and were used for example to find the form of the Student t -distribution. … And in testing large hardware and software systems random inputs are often used. … Random patterns are often used as a way to hide regularities—as in camouflage, security envelopes, and many forms of texturing and distressing.

And in 1963 Alan Robinson suggested the idea of resolution theorem proving, in which one constructs ¬ theorem ∨ axioms , then typically writes this in conjunctive normal form and repeatedly applies rules like ( ¬ p ∨ q) ∧ (p ∨ q)  q to try to reduce it to False , thereby proving given axioms that theorem is True . … But it always seemed that extensive human input—typically from the creators of the system—was needed to make such systems actually find non-trivial proofs.