Checking determinism of regular expressions with counting

Authors:
Haiming Chen;Ping Lu
Affiliations:
State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing, China;State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing, China
Venue:
DLT'12 Proceedings of the 16th international conference on Developments in Language Theory
Year:
2012

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Abstract

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|3) 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.