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Implicit Computational Complexity for Higher Type Functionals

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Computer Science Logic (CSL 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2471))

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Abstract

In previous works we argued that second order logic with comprehension restricted to positive formulas can be viewed as the core of Feasible Mathematics. Indeed, the equational programs over strings that are provable in this logic compute precisely the poly-time computable functions.

Here we investigate the provable functionals of this logic, and show that they are precisely Cook and Urquhart’s basic feasible functionals, BFF. This further confirms the stability of BFF as a notion of computational feasibility in higher type.

Using a formula-as-type morphism, we also show that BFF consists precisely of the functionals that are lambda representable in F 2 restricted to positive type arguments (and trivially augmented with basic constructors and destructors).

Research partially supported by NSF grant CCR-0105651.

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Authors and Affiliations

  1. Computer Science Department, Indiana University, Bloomington, IN 47405

    Daniel Leivant

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  1. Daniel Leivant
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Editors and Affiliations

  1. Laboratory for Foundations of Computer Science Division of Informatics, University of Edinburgh, King’s Buildings, Mayfield Road, Edinburgh, EH9 3JZ, UK

    Julian Bradfield

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Leivant, D. (2002). Implicit Computational Complexity for Higher Type Functionals. In: Bradfield, J. (eds) Computer Science Logic. CSL 2002. Lecture Notes in Computer Science, vol 2471. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45793-3_25

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  • DOI: https://doi.org/10.1007/3-540-45793-3_25

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