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We discuss how much space is sufficient to decide whether a unary given number is a prime. We show that (log log ) 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 ) and also in accept–ASPACE(log log ). Moreover, if the given is composite,...
We propose a new way of characterizing the complexity of online problems.
Instead of measuring the degradation of the output quality caused by the ignorance
of the future we choose to quantify the amount of additional global information
needed for an online algorithm to solve the problem optimally. In our model, the
algorithm cooperates with an oracle that can see the whole input. We define
the advice complexity of the problem to be the minimal number of bits
(normalized per input request, and...
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