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- Title
FOUNDATIONS OF ONLINE STRUCTURE THEORY II: THE OPERATOR APPROACH.
- Authors
DOWNEY, ROD; MELNIKOV, ALEXANDER; KENG MENG NG
- Abstract
We introduce a framework for online structure theory. Our approach generalises notions arising independently in several areas of computability theory and complexity theory. We suggest a unifying approach using operators where we allow the input to be a countable object of an arbitrary complexity. We give a new framework which (i) ties online algorithms with computable analysis, (ii) shows how to use modifications of notions from computable analysis, such as Weihrauch reducibility, to analyse finite but uniform combinatorics, (iii) show how to finitize reverse mathematics to suggest a fine structure of finite analogs of infinite combinatorial problems, and (iv) see how similar ideas can be amalgamated from areas such as EX-learning, computable analysis, distributed computing and the like. One of the key ideas is that online algorithms can be viewed as a sub-area of computable analysis. Conversely, we also get an enrichment of computable analysis from classical online algorithms.
- Subjects
STRUCTURAL analysis (Engineering); OPERATOR theory; ONLINE algorithms; REVERSE mathematics; COMPLEXITY (Philosophy); COMPUTABLE functions
- Publication
Logical Methods in Computer Science (LMCS), 2021, Vol 17, Issue 3, p1
- ISSN
1860-5974
- Publication type
Article
- DOI
10.46298/LMCS-17(3:6)2021