SIGACT News Complexity Theory Column 10
We survey techniques and results obtained over the past thirty years for space-bounded probabilistic computation. We use a common framework for the study of both finite-state automata and logarithmic-space-bounded Turing machines. In particular, we present recent advances on space-efficient deterministic simulation of probabilistic automata.
We give an almost complete classification of empty lattice simplices in dimension 4 using the conjectural results of Mori-Morrison-Morrison, later proved by Sankaran and Bober. In particular, all of these simplices correspond to cyclic quotient singularities, and all but finitely many of them have width bounded by 2.