Are any text formatting markups mandatory (e.g. must there be a '----') for a Wiki?
Is a Wiki without lists a Wiki?
These matters are already dealt with on another page[*], but the short answer is that the key feature of a wiki is the ability for edits to be re-edited. A special case is a wiki used only by yourself. A wiki without a search facility may be awkward to use after a while, but is still a wiki, I suppose. Of course, links to other pages in the wiki must be easily accomplished, and basic markup must be provided for, else you have a wiki so severely handicapped that no-one would want to use it much.
A MinimalWiki must allow for a large (but not necessarily unrestricted) group of people to edit a page, link to other pages, and make new pages. This is typically done with an edit button on each page. There should not be a separate administrative interface (cf. WebLog) to make routine changes.