Encoding the dynamics of deterministic systems

Model reconstruction for discrete deterministic systems

“…In a strongly valid orientation, every clique of K must have a unique sink, and it follows that an orientation is strongly valid if and only if it does not contain a directed cycle of length 3. In particular, any acyclic orientation is strongly valid [7].…”

“…Our main contribution in [7] (based on ideas from [5]) was to prove that there exists a valid orientation for S if and only if the following consistency condition holds:…”

“…In general, neither K nor D show any particular structural properties from a graph-theoretical point of view [7], which turns characterizing valid orientations into a difficult task. Such a characterization was provided for the special class of strongly valid orientations, i.e., orientations which are valid for all networks that share the same transition conflict graph.…”

“…

In a previous paper [7] we proposed a compact model for encoding the dynamic behavior of certain discrete deterministic systems based on extending the widely accepted framework of Petri nets. Here, the problem of reconstructing such a model from experimental data obtained by observation of dynamic processes in the system is addressed.

…”

“…In [7] we consider a class of deterministic systems whose dynamics can be alternatively expressed with the help of a transition selection function trans : X → T . This function assigns to every state x ∈ X a unique transition trans(x) ∈ T (x) that must be switched in order to reach succ(x).…”