Sublinear time algorithms and the average-case complexity of some algorithmic problems in (semi)group theory

We are going to discuss what can be done in sublinear time (in the "length" of an input); in particular, without reading the whole input but only a small part thereof. One well-known example is deciding divisibility of a decimal integer by 2, 5, or 10: this is done by reading just the last digit. We will discuss some less obvious examples from (semi)group theory and show how various fast Las Vegas algorithms, when run in parallel with "honest" algorithms, can reduce the average-case complexity.