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

Hae Sung Eom, Yo Sub Han, Kai Salomaa

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1 Citation (Scopus)


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
Issue number2
Publication statusPublished - 2015 Feb 8


All Science Journal Classification (ASJC) codes

  • Computer Science (miscellaneous)

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