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Tight Bounds for Cut-Operations on Deterministic Finite Automata
Umeå University, Faculty of Science and Technology, Department of Computing Science. (Natural and Formal Languages)ORCID iD: 0000-0001-7349-7693
Universität Giessen.
Universität Giessen.
University of Stellenbosch.
2017 (English)In: Fundamenta Informaticae, ISSN 0169-2968, E-ISSN 1875-8681, Vol. 155, 89-110 p.Article in journal (Refereed) In press
Abstract [en]

We investigate the state complexity of the cut and iterated cut operation for determin- istic finite automata (DFAs), answering an open question stated in [M. BERGLUND, et al.: Cuts in regular expressions. In Proc. DLT, LNCS 7907, 2011]. These operations can be seen as an al- ternative to ordinary concatenation and Kleene star modelling leftmost maximal string matching. We show that the cut operation has a matching upper and lower bound of n states, if m = 1, and (n−1)·m+n states, otherwise, on DFAs accepting the cut of two individual languages that are ac- cepted by n- and m-state DFAs, respectively. In the unary case we obtain max(2n − 1, m + n − 2) states as a tight bound—notice that for m ≤ n the bound for unary DFAs only depends on the former automaton and not on the latter. For accepting the iterated cut of a language accepted by an n-state DFA we find a matching bound of 1+(n+1)·F(1,n+2,−n+2;n+1 | −1) states on DFAs, if n ≥ 4 and where F refers to the generalized hypergeometric function. This bound is in the order of magnitude Θ((n − 1)!). Finally, the bound drops to 2n − 1 for unary DFAs accepting the iterated cut of an n-state DFA, if n ≥ 3, and thus is similar to the bound for the cut operation on unary DFAs.

Place, publisher, year, edition, pages
IOS Press, 2017. Vol. 155, 89-110 p.
Keyword [en]
finite automata, cut and iterated cut operation, descriptional complexity
National Category
Computer Science
Research subject
Computer Science
Identifiers
URN: urn:nbn:se:umu:diva-136263DOI: 10.3233/FI-2017-1577ISI: 000411029200005ISBN: 978-3-319-23111-2 (print)ISBN: 978-3-319-23110-5 (print)OAI: oai:DiVA.org:umu-136263DiVA: diva2:1110075
Available from: 2017-06-15 Created: 2017-06-15 Last updated: 2017-11-02Bibliographically approved

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CiteExportLink to record
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Cite
Citation style
  • apa
  • ieee
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