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An Algebraic Approach to Timed Petri Nets with Applications to Communication Networks
Lingnau, Pascal; Gabriel, Karsten; Modica, Tony
Forschungsberichte der Fakultät IV - Elektrotechnik und Informatik / Technische Universität Berlin
In this report, we define a formalism for a time-extension to algebraic place/transition (P/T) nets. This allows time durations to be assigned to the transitions of a P/T net, representing delays present in the systems that are being modelled, which in turn influence (restrict) the firing behaviour of the nets. This is especially useful when modelling time-dependent systems. The new contribution of this approach is the definition of categories for the timed net classes of timed P/T nets, timed P/T systems and timed P/T states. Moreover, we define functorial relations between these categories as well as functorial relations to categories of untimed P/T nets and systems. The first main result is the formalisation of morphisms for all three net classes that preserve firing behaviour. The second main result is the equivalence of the categories of timed P/T systems and states, establishing a relation between structurally identical nets with a time offset. As a third main result we formalise structuring techniques for timed P/T nets and show that timed P/T nets fit in the framework of M-adhesive categories.
