These theories formalize the quantitative analysis of a number of classical algorithms for the list update problem: 2-competitiveness of move-to-front, the lower bound of 2 for the competitiveness of deterministic list update algorithms and 1.6-competitiveness of the randomized COMB algorithm, the best randomized list update algorithm known to date. The material is based on the first two chapters of Online Computation and Competitive Analysis by Borodin and El-Yaniv.
For an informal description see the FSTTCS 2016 publication Verified Analysis of List Update Algorithms by Haslbeck and Nipkow.
- Haslbeck, M. P. L., & Nipkow, T. (2016). Verified Analysis of List Update Algorithms. Schloss Dagstuhl - Leibniz-Zentrum Fuer Informatik GmbH, Wadern/Saarbruecken, Germany. https://doi.org/10.4230/LIPICS.FSTTCS.2016.49