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Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/13185

Title: Regular Expressions with Counting: Weak versus Strong Determinism
Authors: Gelade, Wouter
Gyssens, Marc
Martens, Wim
Issue Date: 2012
Citation: SIAM JOURNAL ON COMPUTING, 41(1), p. 160-190
Abstract: We study deterministic regular expressions extended with the counting operator. There exist two notions of determinism, strong and weak determinism, which almost coincide for standard regular expressions. This, however, changes dramatically in the presence of counting. In particular, we show that weakly deterministic expressions with counting are exponentially more succinct and strictly more expressive than strongly deterministic ones, even though they still do not capture all regular languages. In addition, we present a finite automaton model with counters, study its properties and investigate the natural extension of the Glushkov construction translating expressions with counting into such counting automata. This translation yields a deterministic automaton if and only if the expression is strongly deterministic. These results then also allow to derive upper bounds for decision problems for strongly deterministic expressions with counting.
URI: http://hdl.handle.net/1942/13185
DOI: 10.1137/100814196
ISI #: 000300892300008
ISSN: 0097-5397
Category: A1
Type: Journal Contribution
Validation: ecoom, 2013
Appears in Collections: Databases and Theoretical Computer Science

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