Feasibility is preserved under limited recursion on notation, because the number of recursive steps is proportional to the binary length of the input rather than to the input value itself.
The actual number or data you put into a calculation or program—for example, the number 1,000,000 has a huge value but a short binary length.
Proportional(as used in mathematical relationships)
Growing or changing at the same rate as something else—if one thing doubles, the other doubles too.
recursion(HCF's characterization of the core property of FLN)
A cognitive universal capacity posited by HCF that underlies not only natural language but also arithmetic (counting and the successor function), and possibly navigation and social relations; not defined over specifically linguistic inputs and outputs.
The availability of such characterizations is often taken to provide additional evidence for the mathematical robustness of classes like \(\textbf{NP}\). 2 generalizes to provide a characterization of the classes which comprise the Polynomial Hierarchy. For instance, the logics \(\Sigma^1_i\) and \(\Pi^1_i\) uniformly capture the complexity classes \(\Sigma^P_i\) and \(\Pi^P_i\) (where \(\mathsf{SO}\exists = \Sigma^1_1\) ). e. full second-order logic) captures \(\textbf{PH}\) itself. On the othe