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The categorical modeling of Petri nets has received much attention recently. The Dialectica construction has also had its fair share of attention. We revisit the use of the Dialectica construction as a categorical model for Petri nets generalizing the original application to suggest that Petri nets with different kinds of transitions can be modeled in the same categorical framework. Transitions representing truth-values, probabilities, rates or multiplicities, evaluated in different algebraic structures called lineales are useful and are modeled here in the same category. We investigate (categorical instances of) this generalized model and its connections to more recent models of categorical nets.
Petri networks and network models are two frameworks for the compositional design of systems of interacting entities. Here we show how to combine them using the concept of a catalyst: an entity that is neither destroyed nor created by any process it
We study detectability properties for labeled Petri nets and finite automata. We first study weak approximate detectability (WAD) that implies that there exists an infinite observed output sequence of the system such that each prefix of the output se
Petri nets, also known as vector addition systems, are a long established model of concurrency with extensive applications in modelling and analysis of hardware, software and database systems, as well as chemical, biological and business processes. T
Godels Dialectica interpretation was designed to obtain a relative consistency proof for Heyting arithmetic, to be used in conjunction with the double negation interpretation to obtain the consistency of Peano arithmetic. In recent years, proof theor
This paper proposes a semi-structural approach to verify the nonblockingness of a Petri net. We construct a structure, called minimax basis reachability graph (minimax-BRG): it provides an abstract description of the reachability set of a net while p