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4
votes
0answers
64 views

Residual for transitive hull

I work in the algebra $R$ of reflexive, transitive relations over some set $S$, ordered by subset inclusion. This is a complete lattice, with intersection as g.l.b. and transitive hull as l.u.b., i.e. ...
1
vote
1answer
138 views

What is DDL (Data Definition Language)?

As a part of my curriculum, I am studying principles of DBMS from the book by Silberschatz and Korth. A part of it is about Data Definition Language (DDL). I ...
7
votes
0answers
152 views

Complete axiomatization of relation algebras without ${}^-$ and $\top$

I'm working on a more thorough algebraic treatment of delta modeling. Briefly, deltas are syntactic entities that can modify products (as in 'software products'). They actually represent relations on ...
4
votes
1answer
146 views

Relation between Kleene star, union and difference in relation algebra

So I'm wondering about some finer points of relation algebra, a field in which I'm not an expert: Given relations $A$, $B$ and $C$ over the same set $S$, is it always true that $A^*\subseteq (B\cup ...
0
votes
1answer
135 views

Euclidean transitive relations

I am currently looking at relations that are both transitive and Euclidean, but not necessarily symmetric, hence not necessarily equivalence relations. I have found nothing about this kind of ...
7
votes
0answers
176 views

Relational model for data structure reasoning

I am trying to find out if there is any work on applying the Codd's relational model (underlying relational databases) for reasoning about linked data structures. Any connections with UML models and ...
0
votes
1answer
118 views

Theory of user control systems?

TL;DR: I am looking for theoretical sources about the different manners to implement user access control. Long version I have almost finished all the stand-alone tools needed in my CMS. I am not ...
4
votes
2answers
386 views

Canonical forms for relational algebra expressions

I'm looking for whatever work may exist, or thoughts people have, on the question of whether/to what extent there exist(s) one or more canonical form(s) to which relational algebra expressions may be ...
11
votes
3answers
573 views

What are recent advances in relational databases?

I'm wondering what are recent advances in relational database theory and related domains? I'm interested in new approaches, query languages (alternatives to SQL and/or extensions to it), products ...
0
votes
1answer
67 views

How to automatically generate indexes and preaggregations from queries

This question might be a little ill-specified, but the idea I want to explore is: User writes a bunch of queries that they want to perform over some data (for concreteness, just consider it a ...
5
votes
1answer
238 views

Definition of a hereditary relation

Sassone, V., Nielsen, M. and Winskel, G. (1996) Models for Concurrency: Towards a Classification. Theoretical Computer Science, 170 (1-2). pp. 297-348., p. 307: Given a tree $S$, define … $\#$ is ...
15
votes
6answers
424 views

Global properties of hereditary classes?

A hereditary class of structures (e.g. graphs) is one that is closed under induced substructures, or equivalently, is closed under vertex removal. Classes of graphs that exclude a minor have nice ...