Unambiguity of SMGL Content Models - Pushdown Automata Revisited

We consider the property of unambiguity for regular expressions, extended by an additional operator &. This denotes concatenation in any order, and must have arbitrary arity since it is not associative. This extension gives us high succinctness in expressing equivalent regular expressions without &. The property of unambiguity means for a regular expression e, that a symbol in a word from its language must not match two diierent occurrences of that symbol in e without lookahead. We extend this notion to &-unambiguity which helps us deal with operator &. We then give a rst method for deciding in polynomial time whether a regular expression with & is &-unambiguous, and if it is, whether it is unambiguous. Our method is constructive | it provides a deterministic automaton with polynomial representation thats accepts the language of the expression, if it is unambiguous and &-unambiguos. If it is only unambiguous then the automaton accepts a subset of the language.