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Category theory has been applied to Petri nets in two distinct ways. The first approach is to define a category whose objects are Petri nets and whose morphisms represent the refinement of one net by another. The second approach is to define a category whose objects are themselves categories representing the possible computations of the net. We establish a close connection between these two...
We present a novel method for proving temporal properties of the behaviour a Petri net. Unlike existing methods, which involve an exhaustive examination of the transition system representing all behaviours of the net, our approach uses morphisms dependent only on the static structure of the net. These morphisms correspond to refinements. We restrict the analysis of dynamic behaviours to particularly...
We establish a precise connection between the two distinct ways in which category theory has been applied to the study of Petri Nets. This connection relates morphisms between nets which consider only their static structure to morphisms on their purely dynamic behaviour, and is based on a CCS-like notion of simulation. We apply these results to the timing of Petri Nets.
We present a sequent calculus for non-commutative intuitionistic linear logic. We prove cut elimination for this calculus and introduce rules for the modality ! (of course). We use a representation theorem for quantales to show that our calculus with ! is sound and complete with respect to a natural class of models, relational quantales. A relational quantale is a quantale whose elements are relations...
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