In the presence of linear order, first-order logic with a least fixed point operator gives P, the problems solvable in deterministic polynomial time.
So, what does "linear order" mean here?
2026-02-23 04:53:25.1771822405
"linear order" in descriptive complexity description of class P
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It just means that the (finite) structures under consideration also have a distinguished linear order relation. (Or, alternatively, the languages always have a distinguished binary relation symbol $\leq$ that is always interpreted to be a linear order.)