State complexity of k-union and k-intersection for prefix-free regular languages

Hae Sung Eom, Yo Sub Han, Kai Salomaa

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

We investigate the state complexity of multiple unions and of multiple intersections for prefix-free regular languages. Prefix-free deterministic finite automata have their own unique structural properties that are crucial for obtaining state complexity upper bounds that are improved from those for general regular languages. We present a tight lower bound construction for k-union using an alphabet of size k + 1 and for k-intersection using a binary alphabet. We prove that the state complexity upper bound for k-union cannot be reached by languages over an alphabet with less than k symbols. We also give a lower bound construction for k-union using a binary alphabet that is within a constant factor of the upper bound.

Original languageEnglish
Pages (from-to)211-227
Number of pages17
JournalInternational Journal of Foundations of Computer Science
Volume26
Issue number2
DOIs
Publication statusPublished - 2015 Jan 1

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Formal languages
Finite automata
Structural properties

All Science Journal Classification (ASJC) codes

  • Computer Science (miscellaneous)

Cite this

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State complexity of k-union and k-intersection for prefix-free regular languages. / Eom, Hae Sung; Han, Yo Sub; Salomaa, Kai.

In: International Journal of Foundations of Computer Science, Vol. 26, No. 2, 01.01.2015, p. 211-227.

Research output: Contribution to journalArticle

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