State complexity of deletion and bipolar deletion

Yo Sub Han; Sang Ki Ko; Kai Salomaa

doi:10.1007/s00236-015-0245-y

State complexity of deletion and bipolar deletion

Yo Sub Han, Sang Ki Ko, Kai Salomaa

College of Computing

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

7 Citations (Scopus)

Abstract

It is well known that the language obtained by deleting an arbitrary language from a regular language is regular. We give an upper bound for the state complexity of deleting an arbitrary language from a regular language and a matching lower bound. We show that the state complexity of deletion is (Formula presented.) [respectively, (Formula presented.) ] when using complete (respectively, incomplete) deterministic finite automata. We show that the state complexity of bipolar deletion has an upper bound (Formula presented.) [respectively (Formula presented.) ] when using complete (respectively, incomplete) deterministic finite automata. In both cases we give almost matching lower bounds.

Original language	English
Pages (from-to)	67-85
Number of pages	19
Journal	Acta Informatica
Volume	53
Issue number	1
DOIs	https://doi.org/10.1007/s00236-015-0245-y
Publication status	Published - 2016 Feb 1

Bibliographical note

Publisher Copyright:
© 2015, Springer-Verlag Berlin Heidelberg.

All Science Journal Classification (ASJC) codes

Software
Information Systems
Computer Networks and Communications

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10.1007/s00236-015-0245-y

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AB - It is well known that the language obtained by deleting an arbitrary language from a regular language is regular. We give an upper bound for the state complexity of deleting an arbitrary language from a regular language and a matching lower bound. We show that the state complexity of deletion is (Formula presented.) [respectively, (Formula presented.) ] when using complete (respectively, incomplete) deterministic finite automata. We show that the state complexity of bipolar deletion has an upper bound (Formula presented.) [respectively (Formula presented.) ] when using complete (respectively, incomplete) deterministic finite automata. In both cases we give almost matching lower bounds.

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State complexity of deletion and bipolar deletion

Abstract

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