As we know, studiyng differences between uniform complexity and nonuniform complexity class is crucial.
For example, P/poly is defined as challenges to derive a separation between P and NP, because P/poly and superpoly-circuit lower bounds gives us the separation.
However, it is possible that P/poly is NOT appropriate to measure the computational ability of uniform P which is defined by usual Turing Machine.
Circuits, branching programs, protocol trees are considerd as physical devices rather than computer programs. Physical devices force to increase the number of "input wires" and can we produce infinitely many devices (and these devices are able to be very very different as the nubmer of input wires increases ) by constant length bit-strings ? It seems that both questions have the answer "NO".
Thus my question is :
(1)Is there any nonuniform (relating with circuits or branching programs) complexity classe C that contains P but P/poly contains the class C.
(2)What is the complexity class which satisfies (1) and is colosest to P as far we know ?