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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 ca ..."
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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...
Petri Net Analysis and Nonmonotonic Reasoning
"... The paper presents a symbolic analysis method for solving bounded deadlock detection and reachability questions for Petri nets using nonmonotonic reasoning techniques. More precisely, a mapping is devised such that given a 1safe P/Tnet, some Boolean conditions on the initial marking, and a bound n ..."
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The paper presents a symbolic analysis method for solving bounded deadlock detection and reachability questions for Petri nets using nonmonotonic reasoning techniques. More precisely, a mapping is devised such that given a 1safe P/Tnet, some Boolean conditions on the initial marking, and a bound n, a logic program is obtained such that there is an execution of at most n steps of the net starting from some initial marking satisfying the conditions leading to deadlock iff the logic program has a stable model. A similar mapping is given for reachability questions from a set of initial markings satisfying given Boolean conditions. Experiments to solve deadlock problems using the Smodels system as the stable model finder indicate that the approach can provide a competitive method for finding short executions to deadlocks.