Rod Downey ; Alexander Melnikov ; Keng Meng Ng - Foundations of Online Structure Theory II: The Operator Approach

lmcs:6641 - Logical Methods in Computer Science, July 21, 2021, Volume 17, Issue 3 - https://doi.org/10.46298/lmcs-17(3:6)2021
Foundations of Online Structure Theory II: The Operator Approach

Authors: Rod Downey ; Alexander Melnikov ; Keng Meng Ng

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.


Volume: Volume 17, Issue 3
Published on: July 21, 2021
Accepted on: December 15, 2020
Submitted on: July 16, 2020
Keywords: Mathematics - Logic,03D78, 68W27


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