Theories of computational complexity
Theories of computational complexity
Machine-independent complexity theory
Handbook of theoretical computer science (vol. A)
Handbook of logic in computer science (vol. 1): background: mathematical structures
Handbook of logic in computer science (vol. 1): background: mathematical structures
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
A Machine-Independent Theory of the Complexity of Recursive Functions
Journal of the ACM (JACM)
On Effective Procedures for Speeding Up Algorithms
Journal of the ACM (JACM)
Speed-Up Theorems in Type-2 Computation
CiE '07 Proceedings of the 3rd conference on Computability in Europe: Computation and Logic in the Real World
Speed-Up Theorems in Type-2 Computation
CiE '07 Proceedings of the 3rd conference on Computability in Europe: Computation and Logic in the Real World
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A classic result known as the speed-up theorem in machine-independent complexity theory shows that there exist some computable functions that do not have best programs for them [2][3]. In this paper we lift this result into type-2 computation under the notion of our type-2 complexity theory depicted in [15][13][14]. While the speed-up phenomenon is essentially inherited from type-1 computation, we cannot directly apply the original proof to our type-2 speed-up theorem because the oracle queries can interfere the speed of the programs and hence the cancellation strategy used in the original proof is no longer correct at type-2. We also argue that a type-2 analog of the operator speed-up theorem [16] does not hold, which suggests that this curious phenomenon disappears in higher-typed computation beyond type-2.