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

Hae Sung Eom, Yo-Sub Han, Kai Salomaa

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

5 Citations (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
Title of host publicationDescriptional Complexity of Formal Systems - 15th International Workshop, DCFS 2013, Proceedings
Pages78-89
Number of pages12
DOIs
Publication statusPublished - 2013 Sep 26
Event15th International Workshop on Descriptional Complexity of Formal Systems, DCFS 2013 - London, ON, Canada
Duration: 2013 Jul 222013 Jul 25

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume8031 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other15th International Workshop on Descriptional Complexity of Formal Systems, DCFS 2013
CountryCanada
CityLondon, ON
Period13/7/2213/7/25

Fingerprint

Prefix-free
State Complexity
Formal languages
Regular Languages
Union
Intersection
Finite automata
Upper bound
Structural properties
Binary
Lower bound
Deterministic Finite Automata
Structural Properties

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Eom, H. S., Han, Y-S., & Salomaa, K. (2013). State complexity of k-union and k-intersection for prefix-free regular languages. In Descriptional Complexity of Formal Systems - 15th International Workshop, DCFS 2013, Proceedings (pp. 78-89). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8031 LNCS). https://doi.org/10.1007/978-3-642-39310-5_9
Eom, Hae Sung ; Han, Yo-Sub ; Salomaa, Kai. / State complexity of k-union and k-intersection for prefix-free regular languages. Descriptional Complexity of Formal Systems - 15th International Workshop, DCFS 2013, Proceedings. 2013. pp. 78-89 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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Eom, HS, Han, Y-S & Salomaa, K 2013, State complexity of k-union and k-intersection for prefix-free regular languages. in Descriptional Complexity of Formal Systems - 15th International Workshop, DCFS 2013, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 8031 LNCS, pp. 78-89, 15th International Workshop on Descriptional Complexity of Formal Systems, DCFS 2013, London, ON, Canada, 13/7/22. https://doi.org/10.1007/978-3-642-39310-5_9

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

Descriptional Complexity of Formal Systems - 15th International Workshop, DCFS 2013, Proceedings. 2013. p. 78-89 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8031 LNCS).

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

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Eom HS, Han Y-S, Salomaa K. State complexity of k-union and k-intersection for prefix-free regular languages. In Descriptional Complexity of Formal Systems - 15th International Workshop, DCFS 2013, Proceedings. 2013. p. 78-89. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-642-39310-5_9