Structural Highness Notions
Wesley Calvert, Johanna N.Y. Franklin, and Dan Turetsky
TL;DR
This paper introduces various highness notions in computability theory related to the complexity of computing isomorphisms between structures, exploring their properties and connections to other problems like Scott analysis and jump hierarchies.
Contribution
It defines new highness notions for degrees concerning isomorphism problems and examines their relationships with classical computability concepts.
Findings
Established several highness notions related to structure isomorphisms
Analyzed variants involving uniformity and negative information
Connected highness notions to Scott analysis and jump hierarchies
Abstract
We introduce several highness notions on degrees related to the problem of computing isomorphisms between structures, provided that isomorphisms exist. We consider variants along axes of uniformity, inclusion of negative information, and several other problems related to computing isomorphisms. These other problems include Scott analysis (in the form of back-and-forth relations), jump hierarchies, and computing descending sequences in linear orders.
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Taxonomy
TopicsComputability, Logic, AI Algorithms · semigroups and automata theory · Benford’s Law and Fraud Detection