State complexity of union and intersection of finite languages

Yo Sub Han, Kai Salomaa

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Citations (Scopus)

Abstract

We investigate the state complexity of union and intersection for finite languages. Note that the problem of obtaining the tight bounds for both operations was open. We compute the upper bounds based on the structural properties of minimal deterministic finite-state automata (DFAs) for finite languages. Then, we show that the upper bounds are tight if we have a variable sized alphabet that can depend on the size of input DFAs. In addition, we prove that the upper bounds are unreachable for any fixed sized alphabet.

Original languageEnglish
Title of host publicationDevelopments in Language Theory - 11th International Conference, DLT 2007 Proceedings
Pages217-228
Number of pages12
Publication statusPublished - 2007 Aug 27
Event11th International Conference on Developments in Language Theory, DLT 2007 - Turku, Finland
Duration: 2007 Jul 32007 Jul 6

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4588 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other11th International Conference on Developments in Language Theory, DLT 2007
CountryFinland
CityTurku
Period07/7/307/7/6

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All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Han, Y. S., & Salomaa, K. (2007). State complexity of union and intersection of finite languages. In Developments in Language Theory - 11th International Conference, DLT 2007 Proceedings (pp. 217-228). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4588 LNCS).