Communication complexity
Efficient randomized pattern-matching algorithms
IBM Journal of Research and Development - Mathematics and computing
Elements of Information Theory (Wiley Series in Telecommunications and Signal Processing)
Elements of Information Theory (Wiley Series in Telecommunications and Signal Processing)
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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 fn, such that either k is greater than fn 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 linear TIME and sub-linear SPACE, whereas finding the exact cycle length cannot be solved in deterministic TIME × SPACE smaller than a constant times n squared. Results involving probabilistic automata and applications to rate-distortion theory and repeated games are also discussed.