scholarly journals Arboricity: An acyclic hypergraph decomposition problem motivated by database theory

2012 ◽  
Vol 160 (1-2) ◽  
pp. 100-107 ◽  
Author(s):  
Yeow Meng Chee ◽  
Lijun Ji ◽  
Andrew Lim ◽  
Anthony K.H. Tung
Keyword(s):  
Decomposition Problem ◽  
Database Theory ◽  
Acyclic Hypergraph

Database theory column

1989 ◽  
Vol 20 (4) ◽  
pp. 17-23 ◽  
Author(s):  
P. Kanellakis ◽  
S. Abiteboul
Keyword(s):  
Database Theory

Database theory column report on Pods 2010

2010 ◽  
Vol 41 (3) ◽  
pp. 86-87
Author(s):  
Dirk Van Gucht
Keyword(s):  
Database Theory

Database theory column

1990 ◽  
Vol 21 (3) ◽  
pp. 9-18 ◽  
Author(s):  
Serge Abiteboul ◽  
Paris Kanellakis
Keyword(s):  
Database Theory

Database Theory Column

2020 ◽  
Vol 51 (3) ◽  
pp. 59-61
Author(s):  
Yufei Tao
Keyword(s):  
Database Theory

Database Theory Column

2016 ◽  
Vol 47 (3) ◽  
pp. 67-68
Author(s):  
Wang-Chiew Tan
Keyword(s):  
Database Theory

A database theory of truth

1988 ◽  
Vol 25 (3) ◽  
pp. 369-379 ◽  
Author(s):  
Vasco Mancini ◽  
Wyllis Bandler
Keyword(s):  
Database Theory

RESTRICTED SETS OF TRAJECTORIES AND DECIDABILITY OF SHUFFLE DECOMPOSITIONS

2005 ◽  
Vol 16 (05) ◽  
pp. 897-912 ◽  
Author(s):  
MICHAEL DOMARATZKI ◽  
KAI SALOMAA
Keyword(s):  
Regular Languages ◽  
Decomposition Problem ◽  
Open Question ◽  
Free Set ◽  
Context Free ◽  
Undecidability Result

The decidability of the shuffle decomposition problem for regular languages is a long standing open question. We consider decompositions of regular languages with respect to shuffle along a regular set of trajectories and obtain positive decidability results for restricted classes of trajectories. Also we consider decompositions of unary regular languages. Finally, we establish in the spirit of the Dassow-Hinz undecidability result an undecidability result for regular languages shuffled along a fixed linear context-free set of trajectories.

scholarly journals The point decomposition problem over hyperelliptic curves

2017 ◽  
Vol 86 (10) ◽  
pp. 2279-2314
Author(s):  
Jean-Charles Faugère ◽  
Alexandre Wallet
Keyword(s):  
Hyperelliptic Curves ◽  
Decomposition Problem

scholarly journals Decomposable Convexities in Graphs and Hypergraphs

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Francesco M. Malvestuto
Keyword(s):  
Convex Hull ◽  
Convex Sets ◽  
Nonempty Subset ◽  
Convex Set ◽  
Convex Geometry ◽  
Convexity Space ◽  
Vertex Set ◽  
Convex Geometries ◽  
Acyclic Hypergraph ◽  
Maximal Clusters

Given a connected hypergraph with vertex set V, a convexity space on is a subset of the powerset of V that contains ∅, V, and the singletons; furthermore, is closed under intersection and every set in is connected in . The members of are called convex sets. The convex hull of a subset X of V is the smallest convex set containing X. By a cluster of we mean any nonempty subset of V in which every two vertices are separated by no convex set. We say that a convexity space on is decomposable if it satisfies the following three axioms: (i) the maximal clusters of form an acyclic hypergraph, (ii) every maximal cluster of is a convex set, and (iii) for every nonempty vertex set X, a vertex does not belong to the convex hull of X if and only if it is separated from X by a convex cluster. We prove that a decomposable convexity space on is fully specified by the maximal clusters of in that (1) there is a closed formula which expresses the convex hull of a set in terms of certain convex clusters of and (2) is a convex geometry if and only if the subspaces of induced by maximal clusters of are all convex geometries. Finally, we prove the decomposability of some known convexities in graphs and hypergraphs taken from the literature (such as “monophonic” and “canonical” convexities in hypergraphs and “all-paths” convexity in graphs).

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