Reconstruction of unknown Petri net structures from asynchronous observations of token change sequences

Abstract

In this paper, we propose an approach for reconstructing Petri net structures from asynchronous observations of token change sequences. In particular, we develop an algorithm that can deal with observations that have finite-length and is able to reconstruct the underlying Petri net structures with complexity that is polynomial in the number of transitions in the net. Note that the observed token change sequences implicitly provide us with information about the initial marking and the number of places in the Petri net. The proposed algorithm is able to find optimal structure(s) in terms of the minimum number of transitions and the minimum number of connections (i.e., the number of nonzero entries in the incident matrix) needed to match the given observations. Furthermore, we develop an updating algorithm to quickly check whether the identified Petri net structure matches future observations.