6 papers
Finite-Query Collapse and Modal Exact Bases in the SCI Hierarchy
Christopher Sorg
We study the exact-basis problem for Solvability Complexity Index (SCI) computational problem families through finite-query transports. A raw finite-query reduction permits arbitra…
Foundational Analysis Of The Solvability Complexity Index: The Weihrauch-SCI Intermediate Hierarchy
Christopher Sorg
The Solvability Complexity Index (SCI) provides an extensional limit-height formalism for recovering a target map from finite samples of an evaluation interface $Î\subseteq\m…
Endpoint Koopman Spectral Computation: Residual Bounds, Instability, and Point-Spectral SCI Calibration Families
Christopher Sorg
We study endpoint Koopman spectral computation from the viewpoint of the Solvability Complexity Index (SCI). Let \((\mathcal X,d)\) be a compact metric space with finite Borel meas…
From Witness-Space Sharpness To Family-Pointwise Exactness For The Solvability Complexity Index
Christopher Sorg
We study how exact Solvability Complexity Index (SCI) statements should be formulated for families of computational problems rather than for single problems. While the equality \(\…
Residual SCI Upper Bounds And Lower Witnesses For Koopman Approximate Point Spectra In For : Extended Version
Christopher Sorg
We study residual computation of approximate point spectral sets of bounded Koopman operators on , , where is a compact…
Computability of the Hahn-Banach Theorem Revisited
Vasco Brattka, Christopher Sorg
Computational properties of the Hahn-Banach theorem have been studied in computable, constructive and reverse mathematics and in all these approaches the theorem is equivalent to w…