Klaus T Aehlig and Arnold Beckmann
APAL 2010, 161(6): 711-736
Publication year: 2010

Using appropriate notation systems for proofs, cut-reduction can often be rendered feasible on these notations, and explicit bounds can be given. Developing a suitable notation system for Bounded Arithmetic, and applying these bounds, all the known results on definable functions of certain such theories can be reobtained in a uniform way.