# Questions tagged [relational-algebra]

the study of relations (i.e., database tables) and relational operators (join, selection, projection, etc.) as a kind of algebraic structure.

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### Type Theory and Principia Mathematica Part IV “Relation Arithmetic”

As type theory is a principle focus of modern computer science, its origins are in Bertrand Russel's theory of types, Principia Mathematica is both the origin of and is expressed in the theory of ...
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### Is there an isomorphism between (subset of) category theory and relational algebra?

It comes from big data perspective. Basically, many frameworks (like Apache Spark) "compensate" lack of relational operations by providing Functor/Monad-like interfaces and there is a similar movement ...
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### How many passes does it take to join 2 relations of fixed size with M buffer blocks?

So let's say 2 relations, B(R) = 200,000 and B(S) = 300,000. The memory buffer is M = 400 blocks. How many passes would this take to join? Notation:
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### Relational algebra for multiple legs of a flight

I'm trying to write the relational algebra for a problem related to this schema: I want to do the following: For each flight list the departure airport code for the first leg of the flight and the ...
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### Relational Algebra obtaining a list of duplicates

I've tried researching, and my best strategy I've got is to attempt to pull out data from the table, and then push the data against itself in order to remove all duplicates, ending up with a table of ...
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### How to find the least optimised database query?

A library uses a relational database to store data about library books, their members and lending (books, which are currently borrowed). The database relations of this system are given below. Lengths ...
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### Joining tables with minimum number of joins

I am working on a generalized problem where I am given only schema definition of multiple tables that i have. Now i have to retrieve certain columns by joining multiple tables such that number of ...
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### Can a $k$-ary relation have polymorphisms of arity greater than $k$?

To quote Hubie Chen's A Rendezvous of Logic, Complexity, and Algebra (2009) on constraint satisfaction and complexity, An operation $f : D^m \to D$ is a polymorphism of a relation $R \subseteq D^k$ ...
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### Proof of RAP-derivation sequence for a set of functional dependencies in relational databases

I'm reading David Maier's outstanding but out-of-print book on relational databases (the book,"The Theory of Relational Databases", is available online from the author's website http://web.cecs.pdx....
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### Count in relational algebra using Ω = { π, σ, ⋈, ⋉, β, x, ∪, ∩ , - }

schema(author)={name, newspaper} The table contains a list of authors. Each author works for a newspaper. So a single newspaper may employ multiple authors. How ...
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### Relational query for universally quantified formula

My university is participating in the implementation of a library borrowing managing system at Richelieu National Library in France. I received the order to formulate the query: "find all users ...
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### NL and NP compute different binary relations, so what?

Let the binary relation computed by a nondeterministic transducer be the relation between input strings and the possible output strings the transducer can produce (and accept) for the given input ...
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### Combinations of elements with mutual relationships

I need to create the combination of 3 elements from a array of given n elements, however every of those 3 el. has to be in "relationship" with each other. Here is an example I can describe my issue ...
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### Using cross-products with relational algebra

I have some questions about something that I'm working on in an assignment for my database class. Here is the schema for the questions I'm working on, so that you know what to refer to: ...
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### A relational algebra extended to model the full DML (“CRUD”) domain

There are multiple references about the relational algebra for modeling queries (SELECT) but I have found very very little on the expanded algebra that would ...
Is there an algorithm to test whether the decomposition of relation $R$ into relations $R_1,\dots,R_n$ is dependency-preserving? In more detail, I am given a relation $R(x_1,\dots,x_m)$ on $m$ ...