Using Petri net invariants in state space construction

The linear algebraic invariant calculus is a powerful technique for the verification of Petri nets. Traditionally it is used for structural verification, i.e. for avoiding the explicit construction of a state space. In this paper, we study the use of Petri net invariants for reducing the memory resources required during state space construction. While place invariants help to reduce the amount of memory needed for each single state (without reducing the number of states as such), transition invariants can be used to reduce the number of states to be stored. Interestingly, our approach does not require computing invariants in full, let alone storing them permanently. All information we need can be deduced from an upper triangular form of the Petri net's incidence matrix. Experiments prove that the place invariant technique leads to improvements in both memory and run time costs while transition invariants lead to a space/time tradeoff that can be controlled heuristically.