In limited recursion on notation, the recursion depth is proportional to the length of y's binary representation rather than to y itself, placing a polynomial bound on the number of recursive calls
A mathematical limit that grows at a controlled, predictable rate (like squaring or cubing a number), rather than exploding exponentially.
Recursion depth(in computer science)
How many times a function calls itself before finishing—like how many Russian nesting dolls you have to open before reaching the smallest one.
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 logic \(\textsf{SO}(\texttt{LFP})\) and \(\textsf{SO}(\texttt{TC})\) are defined analogously by adding these operators to \(\textsf{SO}\) and allowing them to apply to formulas containing second-order variables. e. models \(\mathcal{A}\) for structures interpreting \(\leq\) as a linear order on \(A\)). Immerman (1999, p. 3 as “increas[ing] our intuition that polynomial time is a class whose fundamental nature goes beyond the machine models with which it is usually defined”. e. \(\textbf{P} \