Factoring and testing primes in small space
We discuss how much space is sufficient to decide whether a unary given number n is a prime. We show that O(log log n) space is sufficient for a deterministic Turing machine, if it is equipped with an additional pebble movable along the input tape, and also for an alternating machine, if the space restriction applies only to its accepting computation subtrees. In other words, the language is a prime is in pebble–DSPACE(log log n) and also in accept–ASPACE(log log n). Moreover, if the given n is...