More precisely, these proofs have to be verifiable in polynomial time by a deterministic Turing machine.

Then verification can clearly be done in polynomial time by a deterministic Turing machine.

P: The complexity class of decision problems that can be solved on a deterministic Turing machine in polynomial time.

In a deterministic Turing machine, the set of rules prescribes at most one action to be performed for any given situation.

Solving them on a deterministic Turing machine generally involves super-polynomial runtimes, e.g. c*kn.

P is the class of decision problems that a deterministic Turing machine can solve in polynomial time.

The set of decision problems solvable by a deterministic Turing machine within time f(n).

This forms the basis for the complexity class P, which is the set of decision problems solvable by a deterministic Turing machine within polynomial time.

Similarly, L consists of the languages that can be solved by a deterministic Turing machine with the same assumptions about tape length.

Alternatively, PP can be defined using only deterministic Turing machines.