Q′′

Q′′ is P′′ but it's different. uses a finite number of cells and a finite number of symbol. it was created by User:Yayimhere for no reason at all

syntax

• R, λ, W, U, and T are words in Q′′, which written in mathematical logic is: $\Sigma =\left\{{\text{R,λ,W,U,T}}\right\}$
• if p and q is a words in Q′′ then pq is a word in Q′′
• if q is a word in Q′′ then [q] is a word in Q′′
• only words derivable from these rules are words in Q′′ which can be written in mathematical logic: ${\text{p,q}}\in \Sigma ^{\ast }\supset {\text{pq}}\in \Sigma ^{\ast }\vee {\text{q}}\in \Sigma ^{\ast }\supset [q]\in \Sigma ^{\ast }$

in BNF: <word> ::= R|W|λ|T|<word><word>|[<word>]

semantics

• {a0, a1, a2,... a10} is the tape-alphabet of a Turing machine with a 10 cell tape where each cell is a stack, a₀ being the blank symbol.
• R means move the tape-head leftward one cell wrapping around if at edge.
• λ means replace the top symbol of the stack a_i with a_{Abs(11 mod i + i mod 11)} where the result must be modular base 10(so if i>10 then i=0+the overflow. so if i = 20 then i = 10 since it overflows by 10 and if i=12 then i = 2) then move the tape-head

rightward one cell.

• W move the top of the stack to the bottom
• T pop the top of the stack
• [q] iterate q until the top of the stack is equal to a₀ or if the stack is empty
• U copy the top of the stack