The Complexity of Mu-Formulae on Nets

To use the tableau system, one must have a means of representing sets of states. In the last chapter, we adopted linear inequalities as a presentation language, claiming that this is frequently sufficient. However, in the final example with coverability graphs, we saw a property which depended on a place having an even number of tokens, so showing that linear inequalities are certainly not sufficient even for small nets. The question naturally arises, what language suffices in all cases? That is, what is the expressive power required to represent all the sets of states that may be introduced in a tableau?