Theoretical Computer Science
Space bounded computations: review and new separation results
MFCS '89 Selected papers of the symposium on Mathematical foundations of computer science
Nondeterministic computations in sublogarithmic space and space constructibility
SIAM Journal on Computing
Fast parallel arithmetic via modular representation
SIAM Journal on Computing
ASPACE(o(log log n)) is regular
SIAM Journal on Computing
Bits and relative order from residues, space efficiently
Information Processing Letters
Journal of the ACM (JACM)
Turing Machines with Sublogarithmic Space
Turing Machines with Sublogarithmic Space
Space-Efficient Deterministic Simulation of Probabilistic Automata (Extended Abstract)
STACS '94 Proceedings of the 11th Annual Symposium on Theoretical Aspects of Computer Science
Strong Optimal Lower Bounds for Turing Machines that Accept Nonregular Languages
MFCS '95 Proceedings of the 20th International Symposium on Mathematical Foundations of Computer Science
Uniform Circuits for Division: Consequences and Problems
CCC '01 Proceedings of the 16th Annual Conference on Computational Complexity
One Pebble Versus ε · log n Bits
Fundamenta Informaticae - Non-Classical Models of Automata and Applications
Unary coded NP-complete languages in ASPACE (log log n)
DLT'12 Proceedings of the 16th international conference on Developments in Language Theory
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We discuss how much space is sufficient to decide whether a unary 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. That is, un-Primes is in pebble-DSPACE(log log n) and also in accept-ASPACE(log log n), where un-primes={1 n :n is a prime}. Moreover, if the given n is composite, such machines are able to find a divisor of n. Since O(log log n) space is too small to write down a divisor which might require Ω(log n) bits, the witness divisor is indicated by the input head position at the moment when the machine halts.