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Full-Text Articles in Logic and Foundations
Splitting Theorems In Recursion Theory, Rod G. Downey, Michael Stob
Splitting Theorems In Recursion Theory, Rod G. Downey, Michael Stob
University Faculty Publications and Creative Works
A splitting of an r.e. set A is a pair A1, A2 of disjoint r.e. sets such that A1 ∪ A2 = A. Theorems about splittings have played an important role in recursion theory. One of the main reasons for this is that a splitting of A is a decomposition of A in both the lattice, ε, of recursively enumerable sets and in the uppersemilattice, R, of recursively enumerable degrees (since A1 ≤T A, A2 ≤T A and A ≤T A1 ⊕ A2). Thus splitting theor ems have been used to obtain results about the structure of ε, the structure …
Friedberg Splittings Of Recursively Enumerable Sets, Rod G. Downey, Michael Stob
Friedberg Splittings Of Recursively Enumerable Sets, Rod G. Downey, Michael Stob
University Faculty Publications and Creative Works
A splitting A1{square cup}A2 = A of an r.e. set A is called a Friedberg splitting if for any r.e. set W with W - A not r.e., W - Ai≠0 for i = 1,2. In an earlier paper, the authors investigated Friedberg splittings of maximal sets and showed that they formed an orbit with very interesting degree-theoretical properties. In the present paper we continue our investigations, this time analyzing Friedberg splittings and in particular their orbits and degrees for various classes of r.e. sets.
Only Problems, Not Solutions! (Fourth Edition), Florentin Smarandache
Only Problems, Not Solutions! (Fourth Edition), Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
No abstract provided.
On Matching Ann Structure To Problem Domain Structure, George G. Lendaris, Martin Zwick, Karl Mathia
On Matching Ann Structure To Problem Domain Structure, George G. Lendaris, Martin Zwick, Karl Mathia
Systems Science Faculty Publications and Presentations
To achieve reduced training time and improved generalization with artificial neural networks (ANN, or NN), it is important to use a reduced complexity NN structure. A "problem" is defined by constraints among the variables describing it. If knowledge about these constraints could be obtained a priori, this could be used to reduce the complexity of the ANN before training it. Systems theory literature contains methods for determining and representing structural aspects of constrained data (these methods are herein called GSM, general systems method). The suggestion here is to use the GSM model of the given data as a pattern for …