Introduction to combinators and &lgr;-calculus
Introduction to combinators and &lgr;-calculus
A new recursion-theoretic characterization of the polytime functions
Computational Complexity
A foundational delineation of poly-time
Papers presented at the IEEE symposium on Logic in computer science
Bounded arithmetic, propositional logic, and complexity theory
Bounded arithmetic, propositional logic, and complexity theory
A New Characterization of Type-2 Feasibility
SIAM Journal on Computing
Semantics vs syntax vs computations: machine models for type-2 polynomial-time bounded functionals
Journal of Computer and System Sciences - special issue on complexity theory
Predicative Recurrence in Finite Types
LFCS '94 Proceedings of the Third International Symposium on Logical Foundations of Computer Science
On the Computational Complexity of Type 2 Functionals
CSL '97 Selected Papers from the11th International Workshop on Computer Science Logic
Linear Types and Non Size-Increasing Polynomial Time Computation
LICS '99 Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science
Feasibly constructive proofs and the propositional calculus (Preliminary Version)
STOC '75 Proceedings of seventh annual ACM symposium on Theory of computing
Polynomial time computable arithmetic and conservative extensions
Polynomial time computable arithmetic and conservative extensions
On characterizations of the basic feasible functionals, Part I
Journal of Functional Programming
A proof-theoretic characterization of the basic feasible functionals
Theoretical Computer Science
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Applicative theories form the basis of Feferman's systems of explicit mathematics, which have been introduced in the 1970s. In an applicative universe, all individuals may be thought of as operations, which can freely be applied to each other: self-application is meaningful, but not necessarily total. It has turned out that theories with self-application provide a natural setting for studying notions of abstract computability, especially from a proof-theoretic perspective. This paper is concerned with the study of (unramified) bounded applicative theories which have a strong relationship to classes of computational complexity. We propose new applicative systems whose provably total functions coincide with the functions computable in polynomial time, polynomial space, polynomial time and linear space, as well as linear space. Our theories can be regarded as applicative analogues of traditional systems of bounded arithmetic. We are also interested in higher-type features of our systems; in particular, it is shown that Cook and Urquhart's system PVω is directly contained in a natural applicative theory of polynomial strength.