Checking Determinism of Regular Expressions with Counting

We give characterizations of strong determinism for regular expressions with counting, based on which we present an O(|ΣE ||E|) time algorithm to check whether an expression E with counting is strongly deterministic where ΣE is the set of distinct symbols in E. It improves the previous upper bound of O(|E|) time on the same decision problems for both standard regular expressions and regular expressions with counting. As a natural result of our work we derive a characterization of weak determinism for regular expressions with counting, which leads to a new O(|ΣE ||E|) time algorithm for deciding weak determinism of regular expressions with counting.