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Feasible set functions have small circuits / Arnold, Beckmann

Computability, Volume: 8, Issue: 1, Pages: 67 - 98

Swansea University Author: Arnold, Beckmann

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DOI (Published version): 10.3233/COM-180096

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...

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Published in: Computability
ISSN: 22113568 22113576
Published: 2018
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URI: https://cronfa.swan.ac.uk/Record/cronfa40896
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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.
Keywords: computational complexity, primitive recursive set functions, circuit complexity, Cobham recursive set functions
Issue: 1
Start Page: 67
End Page: 98