[rntz]

^ and $ are a problem, although one with a workaround.

The standard theory of regular expressions focuses entirely on regex matching, rather than searching. For matching, ^ and $ don't really mean anything. In particular, regexp theory is defined in terms of the "language of" a regexp: the set of strings which match it. What's the set of strings that "^" matches? Well, it's the empty string, but only if it comes at the beginning of a line (or sometimes the beginning of the document). This beginning-of-line constraint doesn't fit nicely into the "a regexp is defined by its language/set of strings" theory, much the same way lookahead/lookbehind assertions don't quite fit the theory of regular expressions.

The standard workaround is to augment your alphabet with special beginning/end-of-line characters (or beginning/end-of-document), and say that "^" matches the beginning-of-line character.