How does “inhibitor arc” fit into fundamental equation of Hybrid Petri Nets?

Question

In "ON HYBRID PETRI NETS" by DAVID AND ALLA published in 2001 on page 26 is given an example of how fundamental equation solves a HPN for given start and end time values.

A system looks like

And solution they give looks like

I wonder how fundamental equation shall change if an inhibitor arc is added thus changing HPN into Extended HPN into the system (and there are no conflicts between descreet and continuous transitions)?

Later they provide an example of how to port Extended HPN (p35) into "hybrid automata" yet they never provide any exetsions on how to add inhibitor arc to the fundamental equation.

So I wonder if it is possible to work with EHPN using a fundamental equation to calculate system state at time T or port to hybrid automata would be required for that?

Answer 1

The inhibitor arc is an input with one logic annotation for the computation of the input’s status (annotation) (Hack, 1976). Unlike the “standard” input arc, it does not have a logic annotation for the computation of the mark (annotation) of the input place. The introduction of an inhibitor arc to a model changes the logic annotation for computing the status of the corresponding transition only; it does not add to the computation of the mark of the corresponding place.

If the fundamental equation is used to compute the marks of (input and output) places when transitions fire then the inhibitor arc does not affect the fundamental equation in the computation of marks; there are no changes to the fundamental equation of a model if an inhibitor arc is added to the model.

Reference

Hack, M. Petri Net Languages. Laboratory for Computer Science (formerly Project MAC) Technical Report 159. [Electronic Version]. Massachusetts Institute of Technology, Cambridge, Massachusetts, March 1976. Retrieved on Oct. 5, 2013 at http://publications.csail.mit.edu/lcs/pubs/pdf/MIT-LCS-TR-159.pdf.