This is a web appendix to the following paper, to be presented at ICALP 2024:
A finite presentation of graphs of treewidth at most three, by Amina Doumane, Damien Pous and Samuel Humeau.
Below you can enter a term to see its graph (the syntax is explained at the bottom of this page)
You may move elements using the mouse, or zoom using control-scroll. You may also type commands in the box below to add/remove elements, etc (press 'h' for a list)
| == terms (u,v) == | |
| 0 | empty graph |
| a | a-labeled edge |
| u | v | parallel composition |
| fu | forget u |
| lu | lift u |
| pu | permute p u |
| ru | swap last two sources of u |
| iu | u located according to injection i |
| s(u1,...,uk) | series composition (without the forget) |
| *(u1,...,uk) | star operation |
| u.v | binary sequential composition |
| u' | swap last two sources |
| == sourced terms (at top level only) == | |
| #k u | set arity to k |
| == labels (a) == | |
| s | when s does not start with f/l/s/r, which are reserved for forgets/lifts/series/swaplast |
| -s | when s does so, or when s is empty |
| == permutations (p) == | |
| [231] | explicit permutation of size <=9 |
| (234) | cyclic permutation (here, [1342]), of size <=9 |
| [1,..,8,10,9] | explicit permutation of possibly greater size |
| (9,10) | cyclic permutation of possible greater size |
| (note: the identity permutations cannot be written) | |
| == injections (i) == | |
| {264} | injection mapping 1 to 2, 2 to 6, 3 to 4 |
| {2,6,11} | injection with potentially bigger values |
| {011} | injection mapping 1 to 11 |