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Complexity-Theoretic Hierarchies Induced by Fragments of Gödel’s T

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We introduce two hierarchies of unknown ordinal height. The hierarchies are induced by natural fragments of a calculus based on finite types and Gödel’s T, and all the classes in the hierarchies are uniformly defined without referring to explicit bounds. Deterministic complexity classes like logspace, p, pspace, linspace and exp are captured by the hierarchies. Typical subrecursive classes are also captured, e.g. the small relational Grzegorczyk classes ℰ 0* , ℰ 1* and ℰ 2* .

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  1. Faculty of Engineering, Oslo University College, Oslo, Norway

    Lars Kristiansen

  2. Department of Mathematics, University of Oslo, Oslo, Norway

    Lars Kristiansen

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  1. Lars Kristiansen
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Correspondence to Lars Kristiansen.

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Kristiansen, L. Complexity-Theoretic Hierarchies Induced by Fragments of Gödel’s T . Theory Comput Syst 43, 516–541 (2008). https://doi.org/10.1007/s00224-007-9021-x

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