Foundations of Online Structure Theory II: The Operator Approach.
Logical Methods in Computer Science(2021)
摘要
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. Thus we will begin a view that online algorithms can be viewed as a sub-area of computable analysis. We will 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. Conversely, we also get an enrichment of computable analysis from ideas from the analysis of classical online algorithms.
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关键词
mathematics - logic,03d78, 68w27
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