Say that our Petri net has species S.

Let a _definite state_ to be a mapping from S into \\(\mathbb{N}\\), giving the size of all the populations.

So the set of all definite states is \\(\mathbb{N}^S\\).

Let a _stochastic state_ to be a probability distribution over \\(\mathbb{N}^S\\).

Let a _definite state_ to be a mapping from S into \\(\mathbb{N}\\), giving the size of all the populations.

So the set of all definite states is \\(\mathbb{N}^S\\).

Let a _stochastic state_ to be a probability distribution over \\(\mathbb{N}^S\\).