P-invariants (or place invariants) of Petri Nets can be used to prove mutual exclusion properties.
For more information, see: Apvrille, Ludovic and Saqui-Sannes, Pierre de Static analysis techniques to verify mutual exclusion situations within SysML models. ( In Press: 2013) In: SDL 2013 - 16th International System Design Languages Forum, 26-28 Jun 2013, Montreal, Canada
You can also access to the paper as follows: https://oatao.univ-toulouse.fr/8846/1/Saqui-Sannes_8846.pdf
In the scope of Avatar, P-invariants, or invariants for short, can be used to prove mutual exclusion between states of state machine diagrams. To compute invariants, TTool first translates an Avatar model into a Petri net. Then, it computes the incidence matrix of that Petri net. Finally, it relies on the Farkas algorithm to compute mutual exclusion between states.
Once computed, mutual exclusions are displayed next to each state of the state machine.