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 journalArticlepeer-review

6 Citations (Scopus)


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
Publication statusPublished - 2017 Jun 19

Bibliographical note

Funding Information:
Cho and Han were supported by the Basic Science Research Program through NRF funded by MEST (2015R1D1A1A01060097), the Yonsei University Future-leading Research Initiative of 2016 and the IITP grant funded by the Korea government (MSIP) (R0124-16-0002). Goč, Palioudakis and Salomaa were supported by the Natural Sciences and Engineering Research Council of Canada Grant OGP0147224.

Publisher Copyright:
© 2017 Elsevier B.V.

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)


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