There is No Composition in the Computable Reducibility Degrees
Daniel Mourad
TL;DR
This paper proves that, in the framework of computable reducibility, the composition of two problems does not always correspond to a degree within the reducibility lattice, highlighting a fundamental structural limitation.
Contribution
It establishes that, generally, the composition of problems cannot be represented as a single degree in the computable reducibility lattice, revealing a key structural property.
Findings
No degree corresponds to the composition of two problems in general
Highlights a fundamental limitation in the structure of the computable reducibility lattice
Provides insight into the complexity of problem composition in computability theory
Abstract
We show that, in general, there is no degree corresponding to the composition of two problems in the computable reducibility lattice.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsComputability, Logic, AI Algorithms