Is there any way to check whether a set of gates (for example, take the set comprising of the CNOT gate and the Hadamard gate) is universal for reversible classical computation?
I can think of trial and error methods, like checking whether we can construct a Toffoli gate or a Fredkin gate with our gate set.
But is there a better way --- perhaps a deterministic algorithm --- to check this?
A sufficient condition to check this would be to check whether the gate set is universal for quantum computation. But, there may be gate sets that are universal for reversible classical computation but not universal for quantum computation (for example, the Toffoli gate). How to check these intermediate cases?