We present a Petri net interpretation of the pi-graphs - a graphical variant of the picalculus where recursion and replication are replaced by iteration. The concise and syntax-driven translation can be used to reason in Petri net terms about open reconfigurable systems. We demonstrate that the pi-graphs and their translated high-level Petri nets agree at the semantic level. In consequence, existing results on pi-graphs naturally extend to the translated Petri nets, most notably a guarantee of finiteness by construction.
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The relations between the p-calculus and logic have been less extensively studied than for the l-calculus. We give an account on what can be found in the literature, in two distinct directions: model-checking, and typing. We propose a Curry-Howard correspondence taking into account the dynamic properties of the p-calculus. This is a first presentation of a work in progress.
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