Reasoning about online algorithms with weighted automata

摘要

We describe an automata-theoretic approach for the competitive analysis of online algorithms. Our approach is based on weighted automata, which assign to each input word a cost in R~(≥0). By relating the unbounded look ahead of optimal offline algorithms with nondeterminism, and relating the no look ahead of online algorithms with determinism, we are able to solve problems about the competitive ratio of online algorithms, and the memory they require, by reducing them to questions about determinization and approximated determinization of weighted automata.