Abstract
A survey of certain characterizations of complexity classes in an algebraic, machine-independent manner is presented, together with some applications to weak theories of arithmetic and higher-order functionals. Function algebras are examined, and hierarchies are defined. Bounded arithmetic theories are presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>
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