Learning cycle length through finite automata

Peretz, Ron (2013) Learning cycle length through finite automata. Mathematics of Operations Research, 38 (3). pp. 526-534. ISSN 0364-765X (Submitted)

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Abstract

We study the space-and-time automaton-complexity 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 rate-distortion theory and repeated games are also discussed.

Item Type:	Article
Official URL:	http://mor.journal.informs.org/content/by/year
Additional Information:	© 2013 INFORMS
Divisions:	Mathematics
Subjects:	Q Science > QA Mathematics
Date Deposited:	23 Nov 2012 12:01
Last Modified:	14 Sep 2024 05:42
Projects:	#212/09, FPT/2007-2013, #249159
Funders:	Israel Science Foundation, Google Inter-university center for Electronic Markets and Auctions, European Research Council under the European Community’s Seventh Framework Programme
URI:	http://eprints.lse.ac.uk/id/eprint/47511

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