Arnold Beckmann, Sam Buss, Sy-David Friedman,
Moritz Müller, and Neil Thapen
"Feasible Set Functions Have Small Circuits"
Preprint, December 2016. Revised June 2018.
Former title: "Subset-Bounded Recursion and a Circuit Model for Cobham Recursive Functions"
Abstract: The Cobham Recursive Set Functions (CRSF) provide an analogue of polynomial time computation which applies to arbitrary sets. We give three new equivalent characterizations of CRSF. The first is algebraic, using subset-bounded recursion and a form of Mostowski collapse. The second is our main result: the CRSF functions are shown to be precisely the functions computed by a class of uniform, infinitary, Boolean circuits. The third is in terms of a simple extension of the rudimentary functions by transitive closure and subset-bounded recursion.
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