Before revision:  In STOC'18, Assadi et al. presented a distributed algorithm for maintaining an MIS with O(1) ( amortized) round complexity and O(m^{3/4\left(\log^2 n}\right) \left(\right)  ]  Assadi et al. is deterministic;
After revision:  In STOC'18, Assadi et al. presented a distributed algorithm for maintaining an MIS with O(1) ( perhaps amortized) rounds. Toward initiating a systematic study of dynamic, distributed algorithms, we study some of the most central symmetry-breaking problems: maximal independent set (MIS), maximal matching/(approx-) maximum cardinality matching (MM/MCM), and (\Delta + 1)-vertex coloring. This paper focuses on dynamic, distributed algorithms that are deterministic, and in particular -- robust against an adaptive adversary. Most of our focus is on the MIS algorithm, which achieves O\left(\log^2 n}\right) \left(\right) ] Assadi et al. is deterministic;