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## 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. ...

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

1984
*
Transactions of the American Mathematical Society
*

We specify a

doi:10.2307/1999525
fatcat:7b4ipsjzs5hbxgobaqklcbryby
*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. ...##
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Computational complexity of recursively enumerable sets

1982
*
Information and Control
*

We survey a variety of recent notions and results for classifying the

doi:10.1016/s0019-9958(82)80082-x
fatcat:5hk7aujolrc7xcv3c43acu77rm
*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*. ...##
###
Automorphisms of the lattice of $\Pi _1^0$ classes; perfect thin classes and anc degrees

2001
*
Transactions of the American Mathematical Society
*

The set of strings that have extensions

doi:10.1090/s0002-9947-01-02821-5
fatcat:bpxlye6ar5hufaieoiplhdhtuy
*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. ...##
###
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. ...

##
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Topological aspects of the Medvedev lattice

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*. ...

##
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Every Set has a Least Jump Enumeration

2000
*
Journal of the London Mathematical Society
*

Given a

doi:10.1112/s0024610700001459
fatcat:thdvs2ryvzdvnhjpmkgdbz2s4i
*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. ...##
###
A meta-algorithm for finding large k-plexes

2021
*
Knowledge and Information Systems
*

AbstractWe focus

doi:10.1007/s10115-021-01570-8
fatcat:ktoddg3m5zfh7c555qujtcoliq
*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. ...##
###
Distributed Subgraph Enumeration via Backtracking-based Framework
[article]

2020
*
arXiv
*
pre-print

Instead, it stores the data graph

arXiv:2006.12819v3
fatcat:orfdrbgyozcjrowlsdambm4c5q
*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. ...##
###
Efficient filtering and ranking schemes for finding inclusion dependencies on the web

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

doi:10.1145/2505515.2505722
dblp:conf/cikm/MorishimaYTSK13
fatcat:bwgisnwkerbj7ihelmtaga2gou
*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. ...##
###
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

2015
*
Mathematical proceedings of the Cambridge Philosophical Society (Print)
*

AbstractWe show that a Δ02Turing

doi:10.1017/s0305004115000651
fatcat:lxesnznsxrfcrgi5pmkrs7ujjm
*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 ...##
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Accepting Hybrid Networks of Evolutionary Processors with Special Topologies and Small Communication

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

doi:10.4204/eptcs.31.9
fatcat:u6bbojfdxrcsvf5bmswchz53t4
*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. ...
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