Schnorr randomness and computable randomness are natural concepts of random sequences. However van Lambalgen's Theorem fails for both randomnesses. In this paper we define truth-table Schnorr randomness (defined in [6] too only by martingales) and truth-table reducible randomness, for which we prove
β¦ LIBER β¦
On Schnorr and computable randomness, martingales, and machines
β Scribed by Rod Downey; Evan Griffiths; Geoffrey Laforte
- Publisher
- John Wiley and Sons
- Year
- 2004
- Tongue
- English
- Weight
- 269 KB
- Volume
- 50
- Category
- Article
- ISSN
- 0044-3050
No coin nor oath required. For personal study only.
β¦ Synopsis
Abstract
We examine the randomness and triviality of reals using notions arising from martingales and prefixβfree machines. (Β© 2004 WILEYβVCH Verlag GmbH & Co. KGaA, Weinheim)
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## Abstract For regular sets in Euclidean space, previous work has identified twelve βbasicβ computability notions to (pairs of) which many previous notions considered in literature were shown to be equivalent. With respect to those basic notions we now investigate on the computability of natural o