User blog:LittlePeng9/Intractable problems from hidden information games

(I’ll try to keep everything here as simple as it can be. I may oversimplify some things. Consult with this for more precise results.)

So a while ago I stumbled across a paper (link above) which contained proof that problems solvable by certain type of hidden information machine with space limit of n contains set of problems solvable in time \(2^{2^{…^{2^n}}}\) on deterministic machine, with height of stack determined from exact type of machine. Using time hierarchy theorem, closure of sub-k-EXP functions under taking squares and existence of k-EXPTIME complete problems (trivial example – given description of machine and n in unary does machine halt in \(2^{2^{…^{2^n}}}\) steps with k 2’s in stack?) we can conclude that k-EXPTIME contains problems requiring \(2^{2^{…^{2^n}}}\) steps, thus from these hidden information machines we can find very intractable problems! Furthermore, certain machines are undecidable even under constant space constraint!

Definitions
(Tomorrow)