User:Miui/Pseudo-Catalanian-Jabasys

Abysys(?) is a recipe for taglanging inspired by User:Salpynx, A bliss-pit, Grill Tag, and searching for a mechanism to embed a tag-system inside a group, ideally abelian. Is this meaningful, or possible? Turns out: maybe and yes. (Is this Abelian? As such, this is a fragment of an abelian characteristic i.e pseudo "a quaternion group.")

The system operates through the composition of symbols in two strings: instruction, and state, each a sequence of Johnson solids.

Configuring a tag language

Given this unrestrictive recipe format, a set of constants to keep in mind are CConstant FFactorial GGroup

Given a CFG we can configure a tag language and ```say``` that a configuration is a Thupit.

Group table

Thue(Say) Johnson(¡Characteristic Factor[CF]!)
Catalan(°Characteristic Quotient [CQ]°)

Saying the word 'Thue' is the identity element: grammar. The table above lacks separate headings, but the first row and column represent the identity, so the result of composing two symbols is found by finding the intersection of two symbols by row and column. Order of operation does not matter as this group is abelian, which means the table is symmetrical about the diagonal.

Execution

Each instruction symbol, i, is read in order and composed with the current head, h, of the state string. Instructions are read in a loop. Execution halts when the data string is empty since two symbols are required for composition.

i ∘ h = r

• If the top line is unbroken, the head (leftmost) symbol of the state string is deleted
• If the middle line is unbroken, append (add to right) r ∘ r (i.e. ! (Cofactorial)) to the state-string (this anchors the following appendant)
• If the lower line is also unbroken (anchored by the middle line), append r ∘ i (i.e. h) to the state-string

Computational class and relation to other tag systems

This group contains a subset of symbols that can directly implement Grill Tag.

Converting Grill Tag:

• 10 (command): Use ! (J)
• 11 (command): Use ° (C)
• 0 (data): Use ::= (Say)

See also

• Genera Tag
• https://polytope.miraheze.org/wiki/Near-miss_Johnson_solid#List_of...(generally this recipe is wrong on purpose, an actual power-query is less efficient than a generic queuery based on generic tag principles.)

as formula for jokes

LongDick