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 |