State Complexity of Boundary of Prefix-Free Regular Languages

Hae Sung Eom; Yo Sub Han

doi:10.1142/S0129054115500392

State Complexity of Boundary of Prefix-Free Regular Languages

Hae Sung Eom, Yo Sub Han

Department of Computer Science

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

Recently, researchers studied the state complexity of boundary - L^∗ ∩L^c∗ - of regular languages L motivated from the famous Kuratowski's 14-theorem. Prefix codes - a set of languages - play an important role in several applications. We consider prefix- free regular languages and investigate the state complexity of two operations, L^∗ and L^∗ ∩L^c∗ for prefix-free regular languages. Based on the unique structural properties of a prefix-free minimal DFA, we compute the precise state complexity of L^∗ and L^∗ ∩L^c∗. We then present the tight bound over a quaternary alphabet for L^∗ and L^∗ ∩L^c∗. Our results are smaller than the composition of the state complexity function for individual operations of prefix-free regular languages.

Original language	English
Pages (from-to)	697-707
Number of pages	11
Journal	International Journal of Foundations of Computer Science
Volume	26
Issue number	6
DOIs	https://doi.org/10.1142/S0129054115500392
Publication status	Published - 2015 Sep 1

All Science Journal Classification (ASJC) codes

Computer Science (miscellaneous)

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abstract = "Recently, researchers studied the state complexity of boundary - L∗ ∩Lc∗ - of regular languages L motivated from the famous Kuratowski's 14-theorem. Prefix codes - a set of languages - play an important role in several applications. We consider prefix- free regular languages and investigate the state complexity of two operations, L∗ and L∗ ∩Lc∗ for prefix-free regular languages. Based on the unique structural properties of a prefix-free minimal DFA, we compute the precise state complexity of L∗ and L∗ ∩Lc∗. We then present the tight bound over a quaternary alphabet for L∗ and L∗ ∩Lc∗. Our results are smaller than the composition of the state complexity function for individual operations of prefix-free regular languages.",

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