Title :
A stronger Kolmogorov zero-one law for resource-bounded measure
Author_Institution :
Dept. of Math., Iowa State Univ., Ames, IA
Abstract :
Resource-bounded measure has been defined on the classes E, E2, ESPACE, E2SPACE, REC, and the class of all languages. It is shown here that if C is any of these classes and X is a set of languages that is closed under finite variations and has outer measure less than 1 in C, then X has measure 0 in C. This result strengthens Lutz´s resource-bounded generalization of the classical Kolmogorov zero-one law. It also gives a useful sufficient condition for proving that a set has measure 0 in a complexity class
Keywords :
computational complexity; Kolmogorov zero-one law; complexity class; resource-bounded generalization; resource-bounded measure; Binary sequences; Extraterrestrial measurements; Lifting equipment; Mathematics; Random sequences; Sufficient conditions; Tail;
Conference_Titel :
Computational Complexity, 16th Annual IEEE Conference on, 2001.
Conference_Location :
Chicago, IL
Print_ISBN :
0-7695-1053-1
DOI :
10.1109/CCC.2001.933887
