Covering the Recursive Sets
نویسندگان
چکیده
We give solutions to two of the questions in a paper by Brendle, BrookeTaylor, Ng and Nies. Our examples derive from a 2014 construction by Khan and Miller as well as new direct constructions using martingales. At the same time, we introduce the concept of i.o. subuniformity and relate this concept to recursive measure theory. We prove that there are classes closed downwards under Turing reducibility that have recursive measure zero and that are not i.o. subuniform. This shows that there are examples of classes that cannot be covered with methods other than probabilistic ones. It is easily seen that every set of hyperimmune degree can cover the recursive sets. We prove that there are both examples of hyperimmune-free degree that can and that cannot compute such a cover.
منابع مشابه
Multigranulation single valued neutrosophic covering-based rough sets and their applications to multi-criteria group decision making
In this paper, three types of (philosophical, optimistic and pessimistic) multigranulation single valued neutrosophic (SVN) covering-based rough set models are presented, and these three models are applied to the problem of multi-criteria group decision making (MCGDM).Firstly, a type of SVN covering-based rough set model is proposed.Based on this rough set model, three types of mult...
متن کاملPhylogenetic Analysis of Large Sequence Data Sets
Phylogenetic analysis is an integral part of biological research. As the number of sequenced genomes increases, available data sets are growing in number and size. Several algorithms have been proposed to handle these larger data sets. A family of algorithms known as disc covering methods (DCMs), have been selected by the NSF funded CIPRes project to boost the performance of existing phylogenet...
متن کاملNumber of Minimal Path Sets in a Consecutive-k-out-of-n: F System
In this paper the combinatorial problem of determining the number of minimal path sets of a consecutive-k-out-of-n: F system is considered. For the cases where k = 2, 3 the explicit formulae are given and for k ≥ 4 a recursive relation is obtained. Direct computation for determining the number of minimal path sets of a consecutive-k-out-of-n: F system for k ≥ 4 remains a difficult task. ...
متن کاملRoux-type constructions for covering arrays of strengths three and four
A covering array CA(N ; t, k, v) is an N × k array such that every N × t sub-array contains all t-tuples from v symbols at least once, where t is the strength of the array. Covering arrays are used to generate software test suites to cover all t-sets of component interactions. Recursive constructions for covering arrays of strengths 3 and 4 are developed, generalizing many “Rouxtype” constructi...
متن کاملProducts of Mixed Covering Arrays of Strength Two
A covering array CA(N ; t, k, v) is an N × k array such that every N × t sub-array contains all t-tuples from v symbols at least once, where t is the strength of the array. Covering arrays are used to generate software test suites to cover all t-sets of component interactions. The particular case when t = 2 (pairwise coverage) has been extensively studied, both to develop combinatorial construc...
متن کاملGeneral form of a cooperative gradual maximal covering location problem
Cooperative and gradual covering are two new methods for developing covering location models. In this paper, a cooperative maximal covering location–allocation model is developed (CMCLAP). In addition, both cooperative and gradual covering concepts are applied to the maximal covering location simultaneously (CGMCLP). Then, we develop an integrated form of a cooperative gradual maximal covering ...
متن کامل