# The Complexity of Tiling Problems

## TL;DR

This paper reviews key complexity results in tiling problems, introduces a new deterministic tile set concept, and identifies tiling problems complete for LOGSPACE and NLOGSPACE complexity classes.

## Contribution

It proposes a new definition for deterministic tile sets and characterizes tiling problems complete for specific computational complexity classes.

## Key findings

- Identifies tiling problems complete for LOGSPACE and NLOGSPACE.
- Proposes a formal definition of deterministic tile sets.
- Summarizes major complexity results in tiling problems.

## Abstract

In this document, we collected the most important complexity results of tilings. We also propose a definition of a so-called deterministic set of tile types, in order to capture deterministic classes without the notion of games. We also pinpoint tiling problems complete for respectively LOGSPACE and NLOGSPACE.