Using random sets as oracles
نویسندگان
چکیده
Let R be a notion of algorithmic randomness for individual subsets of N. We say B is a base for R randomness if there is a Z >T B such that Z is R random relative to B. We show that the bases for 1-randomness are exactly the K-trivial sets and discuss several consequences of this result. We also show that the bases for computable randomness include every ∆2 set that is not diagonally noncomputable, but no set of PA-degree. As a consequence, we conclude that an n-c.e. set is a base for computable randomness iff it is Turing incomplete.
منابع مشابه
Forschungsberichte Mathematische Logik Noisy Inference and Oracles Universitt at Heidelberg Mathematisches Institut Noisy Inference and Oracles
A learner noisily infers a function or set, if every correct item is presented innnitely often while in addition some incorrect data ("noise") is presented a nite number of times. It is shown that learning from a noisy informant is equal to nite learning with K-oracle from a usual informant. This result has several variants for learning from text and using diierent oracles. Furthermore, partial...
متن کاملTraining Deterministic Parsers with Non-Deterministic Oracles
Greedy transition-based parsers are very fast but tend to suffer from error propagation. This problem is aggravated by the fact that they are normally trained using oracles that are deterministic and incomplete in the sense that they assume a unique canonical path through the transition system and are only valid as long as the parser does not stray from this path. In this paper, we give a gener...
متن کاملMeasure One Results in Computational Complexity Theory1
Starting with Bennet and Gill’s seminal paper [13] a whole new research line in complexity theory was opened: the examination of relativized complexity theoretic statements which hold for a measure one set of oracles in the measure defined by putting each string into the oracle with probability 12 independent of all other strings (a formal definition is given below). Bennet and Gill were concer...
متن کاملRelationships between NP-sets, Co-NP-sets, and P-sets relative to random oracles
In the present paper we prove that relative to random oracle A (with respect to the uniform measure) the following three assertions hold: (1) there is a pair of disjoint NP A-sets which are separable by no P A-set, (2) there is a pair of disjoint Co-NP A-sets which are separable by no P A-set and (3) there is an innnite Co-NP A-set having no innnite NP A-subset
متن کاملPolynomial-Time Random Oracles and Separating Complexity Classes
Bennett and Gill (1981) showed that P 6= NP 6= coNP for a random oracle A, with probability 1. We investigate whether this result extends to individual polynomial-time random oracles. We consider two notions of random oracles: p-random oracles in the sense of martingales and resource-bounded measure (Lutz, 1992; Ambos-Spies et al., 1997), and p-betting-game random oracles using the betting game...
متن کامل