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## Occurrence Graphs for Interval Timed Coloured Nets.

Berthelot, Gúrard;
Boucheneb, Hanifa
In:
Valette, R.: *Lecture Notes in Computer Science, Vol. 815; Application and Theory of Petri Nets 1994, Proceedings 15th International Conference, Zaragoza, Spain*, pages 79-98.
Springer-Verlag,
1994.

Abstract:
We present an approach to construct the occurrenc e graph for ITCPN
(Interval Timed Coloured Petri Nets). These models, defined by van der
Aalst can simulate other timed Petri nets and allow to describe large and
complex real-time systems. We define classes as sets of states between two
occurrences, and we use these classes to define the occurrenc e graph of
an ITCPN. Then an equivalence relation based on time is defined for
classes, and we show that occurrence graphs reduced using this equivalence
relation are finite if and only if the set of reachable markings is
finite. These graphs can be used to verify all the dynamic properties such
as reachability, boundedness, home, liveness and fairness properties but
also performance properties: minimal and maximal bounds along an
occurrence sequence or a cycle. Finally we complete delay based
equivalence with a colour based equivalence in order to achieve further
reduction

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