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Comment by ulrikrasmussen | Hacker News Reader

Petri nets are a quite general model of concurrency that has also found use in many places in computer science. They are used in model checking, and also as the foundation for giving a semantics to BPMN, for example.

I think it's not unreasonable to consider Petri nets as a generalization of automata (finite or infinite) with concurrency. Just like automata, they find applications in many places depending on how you further extend or restrict them.

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I honestly doubt it will have any practical applications in biology. Computation chemistry and synthetic biology run on differential equations, anything discrete is generally useless. Perhaps it will have some use in a couple of decades when synthetic biology progresses beyond brute force simulations but at the current level it is the wrong abstraction.

You can turn Petri nets into stochastic nets using some formal procedures. Stochastic nets have a "master equation" which spits out a system of PDEs representing reactions where many many things happen at the same time, and so it makes more sense to think in terms of concentrations etc.

We are working to capture this categorically as well. We are perfectly conscious of how a discrete system won't help you if you have an Avogadro number of things going around. Just give us time. :)

We may disagree on this point but thanks for taking the time to reply nonetheless :) I will take a look at your paper.

you have to understand that the real power behind this work is not the Petri nets but that fact that they are described so abstractly that they can take on different shapes, such as stochastic nets, or coloured nets, or...

It puts the different models on the same footing (and hence allowing you to unify tools and do more work)

Also, I'd even argue that biology/chemistry needs to embrace categorical methods and we would see some deep discoveries.

The differential equations are themselves in many cases an abstraction over statistical numbers of discrete events. Arguably, in those cases, they are the wrong abstraction - a thesis which can only be proven by demonstrating the superiority of a different abstraction. Has one been demonstrated? Not yet, for most purposes. Is this a promising avenue of study? IMO, yes.

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