# Computation Theory with Atoms

## Supervisor

## Suitable for

## Abstract

Sets with atoms, also known as nominal sets, are an abstract foundational approach to computing over data structures that are infinite but highly symmetrical, so much so they are finitely presentable and amenable to algorithmic manupulation. Many basic results of classical mathematics and computation theory become more subtle, or even fail, in sets with atoms. For example, in sets with atoms not every vector space has a basis, and a Turing machine may not determinize.

A variety of specific topics are available, aimed at mathematically oriented students.

Prerequisities: Strong mathematical background is essential. Students who enjoy courses such as "Models of Computation", "Categories, Proofs and Processes" or "Computer-Aided Formal Verification" will find this subject suitable.

Some relevant literature:

- M. Bojanczyk: Slightly Infinite Sets. draft available from https://www.mimuw.edu.pl/~bojan/upload/main-6.pdf
- A. Pitts: Nominal Sets: Names and Symmetry in Computer Science. Cambridge University Press, 2013.