Characterising REGEX languages by regular languages equipped with factor-referencing

A (factor-)reference in a word is a special symbol that refers to another factor in the same word; a reference is dereferenced by substituting it with the referenced factor. We introduce and investigate the class ref-REG of all languages that can be obtained by taking a regular language R and then dereferencing all possible references in the words of R. We show that ref-REG coincides with the class of languages defined by regular expressions as they exist in modern programming languages like Perl, Python, Java, etc. (often called REGEX languages).