Structural Approaches for Spn Analysis

Petri nets and Markovian Petri nets are excellent tools for logic and performability system modeling. However, the size of the underlying reachability set is a major limitation in practice. One approach gaining attention among researchers is the use of structured representations, which require us to decompose a net into, or compose a net from, subnets. This paper surveys the stateof-the-art in advanced techniques for storing the reachability set and the transition rate matrix, with particular attention to the use of decision diagrams, Kronecker representations, and their interplay. The conclusion is that, in most practical applications, it is now possible to generate and store enormous reachability sets for logical analysis, while the size of the probability vector being sought is the main limitation when performing the exact solution of the underlying Markov chain.