# What kind of structural features of strings can be described by regular grammars?

Context-free grammars, as well as other types of grammars, can naturally associate structure with the strings of the defined language, for example tree structures in the case of context-free language.

What kind of structural features can be thus described by regular grammars, and associated with the strings of the language.

One answer is of course that it can associate a non-terminals with each prefix (or suffix) of the string. That sorts the prefixes (or suffixes) into sets that may intersect, depending on the grammar. But what else would you see?

related question : Why CFG can specify structure of sentence but Regular grammar cannot?

• You know, I once had an funny thought about the significance of regular languages for which there exist regular expressions that don't rely on the union of subexpressions generating infinite languages; consider the difference between $(a+b)^*$ and $a^* + b^*$, for instance. This would constitute a class of languages smaller than the regular languages, not closed under union, for which the answer to this question would be something like "any repeating pattern"; since the regular languages would be the closure of these languages with union, maybe this answer is "superimposed repeating patterns"? – Patrick87 Feb 20 '14 at 17:19
• For regular languages the best answer is given as the Myhill-Nerode theorem. – Hendrik Jan Feb 20 '14 at 17:23
• @HendrikJan The Myhill-Nerode theorem describes a property of the language, derived from the language itself, not from the grammar. What structural property of the individual strings could be specific of the regular grammar used to define the language. – babou Feb 20 '14 at 17:35