Probabilistic Turing machines already exist. They are a standard extension of TMs that transition from state to state with arbitrary probabilities (not just 0 and 1) and can thus easily generate random bits.
Further, we know that deterministic TMs can do anything that probabilistic TMs can, albeit potentially less efficiently.
I suspect you’re not really rejecting TMs per se, but rather the entire theory of computability and complexity that is standard in CS, more specifically the Church-Turing thesis which is the foundation of the whole thing.
Probabilistic Turing machines already exist. They are a standard extension of TMs that transition from state to state with arbitrary probabilities (not just 0 and 1) and can thus easily generate random bits.
Further, we know that deterministic TMs can do anything that probabilistic TMs can, albeit potentially less efficiently.
I suspect you’re not really rejecting TMs per se, but rather the entire theory of computability and complexity that is standard in CS, more specifically the Church-Turing thesis which is the foundation of the whole thing.