Some Relations Between Subsystems of Arithmetic and Complexity of Computations

We shall introduce a special mode of interactive computations of optimal solutions to optimization problems. A restricted version of such computations was used in [KPT] to show that T 2 i = S 2 i+1 implies ∑ i+2 p = П i+2 p . Here we shall reduce the question whether T 2 i = S 2 i to a question about interactive computations (in a more general sense) of some optimization problems.