An O(n log n) implementation of the standard method for minimizing n-state finite automata
Information Processing Letters
One-unambiguous regular languages
Information and Computation
Finite automata and their decision problems
IBM Journal of Research and Development
Succinctness of regular expressions with interleaving, intersection and counting
Theoretical Computer Science
Foundations of regular expressions in XML schema languages and SPARQL
PhD '12 Proceedings of the on SIGMOD/PODS 2012 PhD Symposium
Descriptional complexity of deterministic regular expressions
MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
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Brüggemann-Klein and Wood have introduced a new family of regular languages, the one-unambiguous regular languages, a very important notion in XML DTDs. A regular language L is one-unambiguous if and only if there exists a regular expression E over the operators of sum, catenation and Kleene star such that L(E) = L and the position automaton of E is deterministic. It implies that for a one-unambiguous expression, there exists an equivalent linear-size deterministic recognizer. In this paper, we extend the notion of one-unambiguity to weak one-unambiguity over regular expressions using the complement operator ¬. We show that a DFA with at most (n + 2) states can be computed from a weakly one-unambiguous expression and that it is decidable whether or not a given DFA recognizes a weakly one-unambiguous language.