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OK, I think I narrowed the 'trick' down. It's actually an interesting existential question. Correct me if I'm wrong but I think the key step is the use of "positive Boolean semantics"; which, as your Ref. 9 proves, are substantially weaker --and hence, unsurprisingly, far more tractable-- than more conventional "stochastic" or "differential" semantics... But then Ref. 9 [1] goes on to make, I think, a frankly astonishing, Church-Turing like existential claim in Biology (Sec 3.2, infra): [...]if a behavior is not possible in the boolean semantics, it is surely not possible in the stochastic semantics whatever the influence forces are. If that is the case, that would IMO have huge consequences! It would mean, then, that some of the underlying machinery of Biology may turn out to be far simpler than we think: no more pesky self-loops or bistable, mutually inhibitory modules to deal with! Tractable network inference, at last! It would potentially revolutionize computational biology, if true. But, is it true? I think I see the intuition, but I don't think the case is as clear-cut, with that single "surely" carrying way too much of the rhetorical work... Indeed, the claim hinges on what I think is a rather interesting, non-trivial existential question: informally, if 'something' (of a given type) cannot be denoted in a certain weaker type, does that mean that 'something' cannot exist? Anyway, not your paper per se; but I think it's an interesting debate nonetheless. [1] https://hal.archives-ouvertes.fr/hal-01378470 |