Translation from Multisingular Hybrid Petri Nets to Multisingular Hybrid Automata

Abstract

In this paper, we investigate some important aspects of a new formalism for modelling and verification of hybrid dynamic systems (HDS), which is called multisingular hybrid Petri nets (MSHPNs). This new hybrid formalism is aimed to bridge the gap between hybrid automata (HA) and hybrid Petri nets (HPNs) by equipping the HPN model with the capabilities of HA to control the execution and firing of timed transitions. Practically, MSHPNs can be considered as the counterpart with the same expressive power as multisingular hybrid automata (MSHA). In order to analyse MSHPN models, a speed-based partitioning technique has been introduced in which the variable space is partitioned based on the balance of continuous places. In this paper, we formalize the notions of conflicts and conflict resolution and the challenging issue of speed computation. Then, we focus on considering a translation from a bounded MSHPN to a multisingular hybrid automaton that preserves the behavioural semantics of the original MSHPN in terms of weak timed bisimulation. The translation algorithm uses the speed-based partitioning method and obtains a speed-based partitioning hybrid automaton for a given bounded MSHPN. Model checking a timed property for an MSHPN amounts to model checking its equivalent property on the obtained speed-based partitioning hybrid automaton, thus MSHPN models can be analysed using the existing tools. The advantages of the proposed method are twofold: (1) hybrid systems can be described more succinctly and therefore more readably as MSHPNs, and (2) one can use the existing tools (like HYTECH) to analyse MSHPN models.