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On the Compositionality and Analysis of Algebraic HighLevel Nets
 RESEARCH REPORT A16, DIGITAL SYSTEMS LABORATORY
, 1991
"... This work discusses three aspects of net theory: compositionality of nets, analysis of nets and highlevel nets. Net theory has often been criticised for the difficulty of giving a compositional semantics to a net. In this work we discuss this problem form a category theoretic point of view. In cate ..."
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This work discusses three aspects of net theory: compositionality of nets, analysis of nets and highlevel nets. Net theory has often been criticised for the difficulty of giving a compositional semantics to a net. In this work we discuss this problem form a category theoretic point of view. In category theory compositionality is represented by colimits. We show how a highlevel net can be mapped into a lowlevel net that represents its behaviour. This construction is functorial and preserves colimits, giving a compositional semantics for these highlevel nets. Using this semantics we propose some proof rules for compositional reasoning with highlevel nets. Linear logic is a recently discovered logic that has many interesting properties. From a net theoretic point of view its interest lies in the fact that it is able to express resources in an analogous manner to nets. Several interpretations of Petri nets in terms of linear logic exist. In this work we study a model theoretic inter...
Transformation of Open and Algebraic HighLevel Petri Net Classes
, 2002
"... The theory based incremental approach to the stepwise development of Petri net process models plays an important role as Petri net based models have been used in many successful applications in practice. This incremental approach is based on the ability to transform a model (by replacing one submode ..."
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The theory based incremental approach to the stepwise development of Petri net process models plays an important role as Petri net based models have been used in many successful applications in practice. This incremental approach is based on the ability to transform a model (by replacing one submodel with another) and to change the class of models (by adding features previously ignored). Formally, these transformations are called net model transformation and net class transformation. This report continues recent research in the area of net class transformations and open Petri nets. It provides a rigorous foundation for the different Petri net classes formalized as categories and the net class transformations formalized as functors in the framework of category theory.