HALOWERKDatenvertragswerk
free inverse monoid munn tree
For a whole original word of0..6 tokens on0=a,1=a^-1,2=b,3=b^-1 (inverse token is XOR1), reconstruct its Munn tree in the rank2 free-group Cayley tree. vertices are ALL distinct freely reduced ORIGINALPREFIX words including emptyroot[], sorted shortlex by length then numeric tokenlex. Return every actual tree edge as arc{from,generator,to}, where generator0=a or1=b is POSITIVE: a prefix-extension by inverse token points its positive-generator arc BACK toward the parent. Arcs sort.
POST https://datenvertrag.halowerk.com/v1/free-inverse-monoid-munn-treeEingaben
| Feld | Typ | Pflicht | Beschreibung |
|---|---|---|---|
| word | Siehe Schema | Ja | |
| claim | Siehe Schema | Ja |
Vollständiges Eingabeschema anzeigen
{
"type": "object",
"properties": {
"word": {
"anyOf": [
{
"type": "array",
"items": {
"type": "integer",
"minimum": 0,
"maximum": 3
},
"minItems": 0,
"maxItems": 6
},
{
"type": "null"
}
]
},
"claim": {
"anyOf": [
{
"type": "object",
"properties": {
"vertices": {
"type": "array",
"items": {
"type": "array",
"items": {
"type": "integer",
"minimum": 0,
"maximum": 3
},
"minItems": 0,
"maxItems": 6
},
"minItems": 1,
"maxItems": 7
},
"arcs": {
"type": "array",
"items": {
"type": "object",
"properties": {
"from": {
"type": "integer",
"minimum": 0,
"maximum": 6
},
"generator": {
"type": "integer",
"minimum": 0,
"maximum": 1
},
"to": {
"type": "integer",
"minimum": 0,
"maximum": 6
}
},
"required": [
"from",
"generator",
"to"
],
"additionalProperties": false
},
"minItems": 0,
"maxItems": 6
},
"endpoint": {
"type": "integer",
"minimum": 0,
"maximum": 6
}
},
"required": [
"vertices",
"arcs",
"endpoint"
],
"additionalProperties": false
},
{
"type": "null"
}
]
}
},
"required": [
"word",
"claim"
],
"additionalProperties": false
}Veröffentlichtes Eingabebeispiel
{
"word": [],
"claim": {
"vertices": [
[]
],
"arcs": [],
"endpoint": 0
}
}Ergebnis & Dokumentation
Maschinenlesbare Dokumentation dieses Hubs
Quelle dieser Seite: der veröffentlichte HALOWERK-Katalog. Stand: 2026-11-07, 02:42 UTC.
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