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Filters
Page 795 of Mathematical Reviews Vol. , Issue 2002B
[page]
2002
Mathematical Reviews
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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
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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
1984
Transactions of the American Mathematical Society
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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
1982
Information and Control
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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
2001
Transactions of the American Mathematical Society
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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
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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
2010
Archive for Mathematical Logic
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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
2000
Journal of the London Mathematical Society
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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
2021
Knowledge and Information Systems
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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]
2020
arXiv
pre-print
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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
2013
Proceedings of the 22nd ACM international conference on Conference on information & knowledge management - CIKM '13
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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
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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
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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)
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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
2010
Electronic Proceedings in Theoretical Computer Science
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2010 pre-print arXiv:1008.1649v1 fatcat:rcydludgbvhsvcappmwlqt37wm
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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