State complexity of permutation on finite languages over a binary alphabet

Da Jung Cho, Daniel Goč, Yo-Sub Han, Sang Ki Ko, Alexandros Palioudakis, Kai Salomaa

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

The set of all strings Parikh equivalent to a string in a language L is called the permutation of L. The permutation of a finite n-state DFA (deterministic finite automaton) language over a binary alphabet can be recognized by a DFA with [formula presented] states. We show that if the language consists of equal length binary strings the bound can be improved to f(n)=[formula presented] and for every n congruent to 1 modulo 3 there exists an n-state DFA A recognizing a set of equal length strings such that the minimal DFA for the permutation of L(A) needs f(n) states.

Original languageEnglish
Pages (from-to)67-78
Number of pages12
JournalTheoretical Computer Science
Volume682
DOIs
Publication statusPublished - 2017 Jun 19

Fingerprint

State Complexity
Deterministic Finite Automata
Finite automata
Permutation
Strings
Binary
Congruent
Modulo
Language

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Cho, Da Jung ; Goč, Daniel ; Han, Yo-Sub ; Ko, Sang Ki ; Palioudakis, Alexandros ; Salomaa, Kai. / State complexity of permutation on finite languages over a binary alphabet. In: Theoretical Computer Science. 2017 ; Vol. 682. pp. 67-78.
@article{26722a9ec7a74d8699c3b4574d5233ed,
title = "State complexity of permutation on finite languages over a binary alphabet",
abstract = "The set of all strings Parikh equivalent to a string in a language L is called the permutation of L. The permutation of a finite n-state DFA (deterministic finite automaton) language over a binary alphabet can be recognized by a DFA with [formula presented] states. We show that if the language consists of equal length binary strings the bound can be improved to f(n)=[formula presented] and for every n congruent to 1 modulo 3 there exists an n-state DFA A recognizing a set of equal length strings such that the minimal DFA for the permutation of L(A) needs f(n) states.",
author = "Cho, {Da Jung} and Daniel Goč and Yo-Sub Han and Ko, {Sang Ki} and Alexandros Palioudakis and Kai Salomaa",
year = "2017",
month = "6",
day = "19",
doi = "10.1016/j.tcs.2017.03.007",
language = "English",
volume = "682",
pages = "67--78",
journal = "Theoretical Computer Science",
issn = "0304-3975",
publisher = "Elsevier",

}

State complexity of permutation on finite languages over a binary alphabet. / Cho, Da Jung; Goč, Daniel; Han, Yo-Sub; Ko, Sang Ki; Palioudakis, Alexandros; Salomaa, Kai.

In: Theoretical Computer Science, Vol. 682, 19.06.2017, p. 67-78.

Research output: Contribution to journalArticle

TY - JOUR

T1 - State complexity of permutation on finite languages over a binary alphabet

AU - Cho, Da Jung

AU - Goč, Daniel

AU - Han, Yo-Sub

AU - Ko, Sang Ki

AU - Palioudakis, Alexandros

AU - Salomaa, Kai

PY - 2017/6/19

Y1 - 2017/6/19

N2 - The set of all strings Parikh equivalent to a string in a language L is called the permutation of L. The permutation of a finite n-state DFA (deterministic finite automaton) language over a binary alphabet can be recognized by a DFA with [formula presented] states. We show that if the language consists of equal length binary strings the bound can be improved to f(n)=[formula presented] and for every n congruent to 1 modulo 3 there exists an n-state DFA A recognizing a set of equal length strings such that the minimal DFA for the permutation of L(A) needs f(n) states.

AB - The set of all strings Parikh equivalent to a string in a language L is called the permutation of L. The permutation of a finite n-state DFA (deterministic finite automaton) language over a binary alphabet can be recognized by a DFA with [formula presented] states. We show that if the language consists of equal length binary strings the bound can be improved to f(n)=[formula presented] and for every n congruent to 1 modulo 3 there exists an n-state DFA A recognizing a set of equal length strings such that the minimal DFA for the permutation of L(A) needs f(n) states.

UR - http://www.scopus.com/inward/record.url?scp=85017111531&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85017111531&partnerID=8YFLogxK

U2 - 10.1016/j.tcs.2017.03.007

DO - 10.1016/j.tcs.2017.03.007

M3 - Article

VL - 682

SP - 67

EP - 78

JO - Theoretical Computer Science

JF - Theoretical Computer Science

SN - 0304-3975

ER -