A Foundational Delineation of Poly-time

We show that a function over {0, 1}* is poly-time iff it is computed by an equational program which can be proved to be everywhere converging in constructive second-order logic with set-existence (comprehension) restricted to positive quantifier-free formulas, or alternatively with set-existence for positive existential formulas. These set-existence principles convey an ontology of infinite sets as evolving, not completed, totalities. Our characterization results can consequently be viewed as a foundational justification for identifying poly-time with feasibility.

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