Filters








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Page 795 of Mathematical Reviews Vol. , Issue 2002B [page]

2002 Mathematical Reviews  
By “filter” we mean a filter F on the set w of natural numbers, containing all cofinite sets. If f:w— is a finite-to-one map, then f(#) is defined as {¥ Caw: f~'(X)€F}; it is a filter if F is.  ...  Similarly, we may de- fine a computably enumerable vector space. G. Metakides and A. Nerode [Ann. Math.  ... 

Page 9 of Mathematical Reviews Vol. 52, Issue 1 [page]

1976 Mathematical Reviews  
filters in the lattice of all finitary recursively enumerable relations.  ...  Theorem: Let F be a realizability filter in the lattice of all recur- sively enumerable sets.  ... 

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  
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.  ...  defined.  ...  If x > bse] and Fe is not yet satisfied, compute Ap(s) and if As\ x * A {s)\ x enumerate x in B. Step 2 (to code A into 77). For each x ^. As -As_x, enumerate bsx~ ' in 77.  ... 
doi:10.2307/1999525 fatcat:7b4ipsjzs5hbxgobaqklcbryby

Computational complexity of recursively enumerable sets

Robert I. Soare
1982 Information and Control  
We survey a variety of recent notions and results for classifying the computational complexity of a recursively enumerable (r.e.) set.  ...  These complexity theoretic notions are shown to be equivalent to various recursion theoretic notions and are used to relate the complexity properties of an r.e. set A to its algebraic structure in the  ...  decomposition of R into two classes one of which is a definable ideal and the other a definable filter.  ... 
doi:10.1016/s0019-9958(82)80082-x fatcat:5hk7aujolrc7xcv3c43acu77rm

Automorphisms of the lattice of $\Pi _1^0$ classes; perfect thin classes and anc degrees

Peter Cholak, Richard Coles, Rod Downey, Eberhard Herrmann
2001 Transactions of the American Mathematical Society  
The set of strings that have extensions in C is a co-computably enumerable set. Therefore we define deg T (C) to be the degree of this co-c.e. set.  ...  In this paper we study this lattice and its connection with the computably enumerable degrees, along the same lines as the well known Post program for the computably enumerable sets.  ...  Alongside of computably enumerable sets and degrees, Π 0 1 class occupy a position as a fundamental notion in computability theory.  ... 
doi:10.1090/s0002-9947-01-02821-5 fatcat:bpxlye6ar5hufaieoiplhdhtuy

Page 638 of Mathematical Reviews Vol. , Issue 89B [page]

1989 Mathematical Reviews  
One of the main open questions in recursion theory is whether the jump operation (or the degree 0’) is first-order definable in the partial ordering of degrees.  ...  In this paper we propose another natural gen- eralization. On the basis of the theory of enumerations we define the notion of constructive nonmorphism of enumerated sets, CNM for short.  ... 

Topological aspects of the Medvedev lattice

Andrew E. M. Lewis, Richard A. Shore, Andrea Sorbi
2010 Archive for Mathematical Logic  
On the other hand, Medvedev reducibility, whose degree structure gives rise to the Medvedev lattice, provides a novel computability-theoretic reducibility paradigm which is interesting in its own right  ...  filter generated by the nonzero discrete degrees.  ...  A few remarks on degrees of enumerability A set A is of quasi-minimal e-degree if A is not c.e. and for every total function f , if f ≤ e A then f is computable.  ... 
doi:10.1007/s00153-010-0215-6 fatcat:qsw6kfbj7bcydcug2lsgi5xbiu

Every Set has a Least Jump Enumeration

Richard J. Coles, Rod G. Downey, Theodore A. Slaman
2000 Journal of the London Mathematical Society  
Given a computably enumerable set B, there is a Turing degree which is the least jump of any set in which B is computably enumerable, namely 0 .  ...  Remarkably, this is not a phenomenon of computably enumerable sets.  ...  For background on forcing arguments in computability theory we direct the reader to Lerman [2] . We now define our notion of forcing.  ... 
doi:10.1112/s0024610700001459 fatcat:thdvs2ryvzdvnhjpmkgdbz2s4i

A meta-algorithm for finding large k-plexes

Alessio Conte, Donatella Firmani, Maurizio Patrignani, Riccardo Torlone
2021 Knowledge and Information Systems  
AbstractWe focus on the automatic detection of communities in large networks, a challenging problem in many disciplines (such as sociology, biology, and computer science).  ...  In this paper we tackle the problem of finding only large k-plexes (i.e., comparable in size to the largest clique) and design a meta-algorithm that can be used on top of known enumeration algorithms to  ...  The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material.  ... 
doi:10.1007/s10115-021-01570-8 fatcat:ktoddg3m5zfh7c555qujtcoliq

Distributed Subgraph Enumeration via Backtracking-based Framework [article]

Zhaokang Wang, Weiwei Hu, Chunfeng Yuan, Rong Gu, Yihua Huang
2020 arXiv   pre-print
Instead, it stores the data graph in a distributed database. Each task queries adjacency sets of the data graph on demand.  ...  Each task enumerates subgraphs around a vertex in the data graph, guided by a backtracking-based execution plan. B-BENU does not shuffle any partial matching result.  ...  B-BENU supports integrating other filtering techniques like the degree filter by adding corresponding filtering conditions.  ... 
arXiv:2006.12819v3 fatcat:orfdrbgyozcjrowlsdambm4c5q

Efficient filtering and ranking schemes for finding inclusion dependencies on the web

Atsuyuki Morishima, Erika Yumiya, Masami Takahashi, Shigeo Sugimoto, Hiroyuki Kitagawa
2013 Proceedings of the 22nd ACM international conference on Conference on information & knowledge management - CIKM '13  
This paper presents the results of a first comprehensive study on finding inclusion dependencies on the Web.  ...  First, we propose a bit-based signature scheme to efficiently select candidates (element pairs) in the enumeration process.  ...  Mitsuharu Nagamori for the discussion in seminars.  ... 
doi:10.1145/2505515.2505722 dblp:conf/cikm/MorishimaYTSK13 fatcat:bwgisnwkerbj7ihelmtaga2gou

Page 5252 of Mathematical Reviews Vol. , Issue 91J [page]

1991 Mathematical Reviews  
Ziegler, in Model-theoretic logics, 557-577, Springer, New York, 1985; see MR 87g:03033]. Let D be a filter on J.  ...  In the last two theorems he assumes that the filters extend the corresponding filter of cofinite sets and proves that a wide class of sentences is preserved under topological products.  ... 

Page 1635 of Mathematical Reviews Vol. , Issue 81E [page]

1981 Mathematical Reviews  
Here relative recursiveness between elements x, y of “coded” filter spaces is defined in terms of enumeration operators 81e:03047  ...  Alongside the main theory, the author develops a secondary theme concerning the study of the induced topology on a filter space.  ... 

The finite intersection principle and genericity

DAVID DIAMONDSTONE, ROD DOWNEY, NOAM GREENBERG, DAN TURETSKY
2015 Mathematical proceedings of the Cambridge Philosophical Society (Print)  
AbstractWe show that a Δ02Turing degree computes solutions to all computable instances of the finite intersection principle if and only if it computes a 1-generic degree.  ...  Thus, any degree which can enumerate a 1-generic filter for P A can compute a maximal solution for A. We show that any 1-generic set (in the Cohen sense) does.  ...  They also showed that the degrees in the following collections are all FIP-degrees: ‚ nonzero computably enumerable (c.e.) degrees; ‚ degrees which are not 0 1 -dominated; ‚ degrees that compute generics  ... 
doi:10.1017/s0305004115000651 fatcat:lxesnznsxrfcrgi5pmkrs7ujjm

Accepting Hybrid Networks of Evolutionary Processors with Special Topologies and Small Communication

Jürgen Dassow, Florin Manea
2010 Electronic Proceedings in Theoretical Computer Science  
Starting from the fact that complete Accepting Hybrid Networks of Evolutionary Processors allow much communication between the nodes and are far from network structures used in practice, we propose in  ...  For star networks or grid networks, we show a more general result; that is, each recursively enumerable language can be accepted efficiently by a star- or grid-AHNEP.  ...  -α : X G −→ { * , l, r}; α(x) gives the action mode of the rules of node x on the words existing in that node. β : X G −→ {(s), (w)} defines the type of the input/output filters of a node.  ... 
doi:10.4204/eptcs.31.9 fatcat:u6bbojfdxrcsvf5bmswchz53t4
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