The measure you are trying to minimize is called (directed) bandwidth. Finding a minimum directed bandwidth ordering is NP-hard.


Linear (used the same way as in linear extensions) refers to the fact that the semantic model is an infinite "path" ("linear", if you will) without cycles; every state has a well-defined next element. There is a total ordering over the Kripke-structure (possible worlds). I.e. it refers to temporal.

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