Deterministic Regular Expressions withźInterleaving

We study the determinism checking problem for regular expressions extended with interleaving. There are two notions of determinism, i.e., strong and weak determinism. Interleaving allows child elements intermix in any order. Although interleaving does not increase the expressive power of regular expressions, its use makes the sizes of regular expressions be exponentially more succinct. We first show an $$\mathcal {O}|\varSigma ||E|$$ time algorithm to check the weak determinism of such expressions, where $$\varSigma $$ is the set of distinct symbols in the expression. Next, we derive an $$\mathcal {O}|E|$$ method to transform a regular expression with interleaving to its weakly star normal form which can be used to rewrite an expression that is weakly but not strongly deterministic into an equivalent strongly deterministic expression in linear time. Based on this form, we present an $$\mathcal {O}|\varSigma ||E|$$ algorithm to check strong determinism. As far as we know, they are the first $$\mathcal {O}|\varSigma ||E|$$ time algorithms proposed for solving the weak and strong determinism problems of regular expressions with interleaving.