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Some recent research directions in the computably enumerable sets [article]

Peter Cholak
2013 arXiv   pre-print
As suggested by the title, this paper is a survey of recent results and questions on the collection of computably enumerable sets under inclusion.  ...  This is not a broad survey but one focused on the author's and a few others' current research.  ...  The following definition depends on the chosen enumeration of all c.e. sets.  ... 
arXiv:1312.5979v1 fatcat:mxijl7gcbrc7lhpdzeoroyaxse

Some Recent Research Directions in the Computably Enumerable Sets [chapter]

Peter A. Cholak
2017 The Incomputable  
As suggested by the title, this paper is a survey of recent results and questions on the collection of computably enumerable sets under inclusion.  ...  This is not a broad survey but one focused on the author's and a few others' current research. There are many equivalent ways to definite a computably enumerable or c.e. set.  ...  The following definition depends on the chosen enumeration of all c.e. sets.  ... 
doi:10.1007/978-3-319-43669-2_5 fatcat:e4jovc3kvfhhdfhkigcbpch5ze

Page 807 of Mathematical Reviews Vol. , Issue 2003B [page]

2003 Mathematical Reviews  
of prompt and low computably enumerable sets.  ...  This paper presents two groups of results on automorphisms of computably enumerable (c.e.) sets, linking degree-theoretic and dynamic properties of c.e. sets: 1.  ... 

Definable Encodings in the Computably Enumerable Sets

Peter A. Cholak, Leo A. Harrington
2000 Bulletin of Symbolic Logic  
The purpose of this communication is to announce some recent results on the computably enumerable sets.  ...  All sets will be computably enumerable non-computable sets and all degrees will be computably enumerable and non-computable, unless otherwise noted.  ...  All sets will be computably enumerable non-computable sets and all degrees will computably enumerable and non-computable, unless otherwise noted.  ... 
doi:10.2307/421206 fatcat:oekr3krowrhy7gfo62tpxpvahi

The Complexity of Orbits of Computably Enumerable Sets

Peter A. Cholak, Rodney Downey, Leo A. Harrington
2008 Bulletin of Symbolic Logic  
The goal of this paper is to announce there is a single orbit of the c.e. sets with inclusion, ε, such that the question of membership in this orbit is complete.  ...  This result and proof have a number of nice corollaries: the Scott rank of ε is + 1; not all orbits are elementarily definable; there is no arithmetic description of all orbits of ε; for all finite α ≥  ...  There is a property S(A), a prompt low degree d 1 , a prompt high 2 degree d 2 greater than d 1 , and tardy high 2 degree e such that for all E ≤ T e, ¬S(E) and if d 1 ≤ T D ≤ T d 2 then S(D).  ... 
doi:10.2178/bsl/1208358844 fatcat:frqyk375tfbepbii74zfrqwski

JSL volume 67 issue 2 Cover and Front matter

2002 Journal of Symbolic Logic (JSL)  
FERNANDES and FERNANDO On orbits, pf prompt and low computably enumerable sets, by KEVIN WALD . 649 Definable incompleteness and Friedberg splittings, by RUSSELL MILLER 679 Degree spectra of relations  ...  Continued on inside back cover 10 9 8 7 6 5 4 3 2 1 07 06 05 04 03 02 -- TABLE OF CONTENTS OF Congruence relations on lattices of recursively enumerable sets, by TODD Quelques proprietes des theories de  ... 
doi:10.1017/s0022481200009555 fatcat:jledthgadjenrmxcg6vxfdb4le

Friedberg splittings of recursively enumerable sets

Rod Downey, Michael Stob
1993 Annals of Pure and Applied Logic  
Downey, R. and M. Stob, Friedberg splittings of recursively enumerable sets, Annals of Pure and Applied Logic 59 (1993) 175-199.  ...  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.  ...  Further assume that f is monotone and we can assume enumerations of r.e. sets so that at most one element enters at most one set at one stage. We will define a function g.  ... 
doi:10.1016/0168-0072(93)90092-r fatcat:v2eb3cqujfbqngqwgd6wltnqte

On n-Tardy Sets [article]

Peter A. Cholak, Peter M. Gerdes, Karen Lange
2010 arXiv   pre-print
Since they also showed no 2-tardy set is complete, Harrington and Soare showed that there exists an orbit of computably enumerable sets such that every set in that orbit is incomplete.  ...  Our study of n-tardy sets takes off from where Harrington and Soare left off. We answer all the open questions asked by Harrington and Soare about n-tardy sets.  ...  ., not of prompt degree) sets A such that every degree Turing above A is almost prompt, (see [5, Theorem 11.8]) and that the join of an almost prompt set and any computably enumerable set is almost prompt  ... 
arXiv:1101.0228v1 fatcat:nwuuedkexnairlmfx4w7aubdhq

An Algebraic Decomposition of the Recursively Enumerable Degrees and the Coincidence of Several Degree Classes with the Promptly Simple Degrees

Klaus Ambos-Spies, Carl G. Jockusch, Richard A. Shore, Robert I. Soare
1984 Transactions of the American Mathematical Society  
a low r.e. degree; SPH, the degrees of non-Wi-simple r.e. sets with the splitting property; and G, the degrees in the orbit of an r.e. generic set under automorphisms of the lattice of r.e. sets. 0.  ...  We specify a definable decomposition of the upper semilattice of recursively enumerable (r.e.) degrees R as the disjoint union of an ideal M and a strong filter NC.  ...  These equivalences were discovered by studying the degrees of promptly simple sets, a computational complexity analogue of Post's simple set introduced by Maass [1982] for studying orbits of r.e. sets  ... 
doi:10.2307/1999525 fatcat:7b4ipsjzs5hbxgobaqklcbryby

On n-tardy sets

Peter A. Cholak, Peter M. Gerdes, Karen Lange
2012 Annals of Pure and Applied Logic  
Since they also showed no 2-tardy set is complete, Harrington and Soare showed that there exists an orbit of computably enumerable sets such that every set in that orbit is incomplete.  ...  Our study of n-tardy sets takes off from where Harrington and Soare left off. We answer all the open questions asked by Harrington and Soare about n-tardy sets.  ...  Acknowledgements The first author was partially supported by NSF DMS-0652669 and NSF-DMS-0800198. The second author was partially supported by NSF EMSW21-RTG-0739007 and EMSW21-RTG-0838506.  ... 
doi:10.1016/j.apal.2012.02.001 fatcat:ktio65bwnned7coi4wreegc67i

Orbits of computably enumerable sets: low sets can avoid an upper cone

Russell Miller
2002 Annals of Pure and Applied Logic  
We investigate the orbit of a low computably enumerable (c.e.) set under automorphisms of the partial order E of c.e. sets under inclusion.  ...  Thus, the orbit in E of the low set A cannot be contained in the upper cone above C.  ...  Lemmas 17 and 18 together show that G A =Ĝ B . Lemma 15 shows that C T B. Along with Lemmas 13 and 14 and Theorem 4, this completes the proof of Theorem 1.  ... 
doi:10.1016/s0168-0072(01)00119-1 fatcat:skffmxyfrfdclane7tt3kadsny

Channel Access Client Toolbox for Matlab [article]

Andrei Terebilo
2002 arXiv   pre-print
Another purpose of this paper is to propose a feasible path to a synergy between accelerator control systems and accelerator simulation codes, the idea also known as on-line accelerator model.  ...  The benefits include: the ability to calculate and display parameters that use Epics process variables as inputs, availability of Matlab graphics tools for user interface design, and integration with Matlab-based  ...  ACKNOWLEDGEMENTS The work reported on here was supported in part by DOE Contract DE-AC03-76SF00515 and Office of Basic Energy Sciences, Division of Chemical Sciences.  ... 
arXiv:physics/0111198v2 fatcat:6kngv6e4j5br5d7zngqim226ne

Experiments with Human Integration in Asynchronous and Sequential Multi-agent Frameworks for Architecture Optimization

Nozomi Hitomi, Daniel Selva
2015 Procedia Computer Science  
In order to achieve a beneficial cooperation between humans and computers, this paper discusses and compares two different modes of a multi-agent optimization framework (asynchronous and sequential) that  ...  attempt to integrate human and computational agents in a hyper-heuristic architecture optimization algorithm.  ...  of orbits in O, including both the empty set (i.e., no orbits) and the universal set (i.e., all orbits).  ... 
doi:10.1016/j.procs.2015.03.024 fatcat:lhf7bok4bvbbfjh6o42ligiqti

Multiperiodic orbits from interacting soft spots in cyclically-sheared amorphous solids [article]

Nathan C. Keim, Joseph D. Paulsen
2021 arXiv   pre-print
Motivated by the mesoscopic features of displacement fields in experiments on jammed solids, we propose and analyze a simple model of interacting soft spots -- locations where particles rearrange under  ...  We suggest directions for seeking this signature of frustration in experiments, and we describe how to achieve it in designed systems.  ...  To obtain this set, for each of the 2 N possible states, we compute the two values of H that bound the interval of stability for the state.  ... 
arXiv:2101.01240v1 fatcat:bbydu6cmang2zefjhkzcpz3eta

Multiperiodic orbits from interacting soft spots in cyclically sheared amorphous solids

Nathan C. Keim, Joseph D. Paulsen
2021 Science Advances  
Motivated by mesoscopic features of displacement fields in experiments on jammed solids, we propose and analyze a simple model of interacting soft spots—locations where particles rearrange under stress  ...  We suggest directions for seeking this signature of frustration in experiments and for achieving it in designed systems.  ...  Lindeman and S. R. Nagel for bringing to our attention  ... 
doi:10.1126/sciadv.abg7685 fatcat:hymyqoxsj5asrdzfc2eip7vkxy
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