User:Yayimhere/iLGwMLS

iLGwMLS is a class of problems. Lets get these definitions:

• K is a program.

• Mi is the memory of K at iteration.

• |x| is the length of x.

• A is the input string.

• Ni is the time between two iterations Mi and Mi+1.

• S is the output of K.

• h is the "halt code".

• hα is the iteration where K halts.

• xy is the inputs concatenated.

Now, K has the following properties:

• f(x) = x*a+b a,b ∈ R

• |M0| = |A|.

• |Mi| = fi(|A|).

• Ni ≥ |Mi|.

• K halts when fi(|A|) ≤ h.

• S = M0M1...Mhα-1Mhα

Then, we notate the set of programs that satisfy these conditions for f as fω. Then, T* is the set of problems solveable by a program in T. Now, iLGwMLS is the union of all fω* for linear f.