Peretz, Ron
(2013)
Learning cycle length through finite automata.
Mathematics of Operations Research, 38 (3).
pp. 526534.
ISSN 0364765X
(Submitted)
Abstract
We study the spaceandtime automatoncomplexity of two related problems concerning the cycle length of a periodic stream of input bits. One problem is to find the exact cycle length of a periodic stream of input bits provided that the cycle length is bounded by a known parameter n. The other problem is to find a large number k that divides the cycle length. By \large" we mean that there is an unbounded increasing function f(n), such that either k is greater than f(n) or k is the exact cycle length. Our main results include that finding a large divisor of the cycle length can be solved in deterministic SPACE o(n) and TIME O(n), whereas finding the exact cycle length cannot be solved in deterministic TIME X SPACE smaller than (n2). Results involving probabilistic automata and applications to ratedistortion theory and repeated games are also discussed.
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