On Simon’s Congruence Closure of a String

Sungmin Kim, Yo Sub Han, Sang Ki Ko, Kai Salomaa

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

1 Citation (Scopus)


Two strings are Simon’s ∼ k -congruent if they have the same set of subsequences of length at most k. We study the Simon’s congruence closure of a string, which is regular by definition. Given a string w over an alphabet Σ, we present an efficient DFA construction that accepts all ∼ k -congruent strings with respect to w. We also present lower bounds for the state complexity of the Simon’s congruence closure. Finally, we design a polynomial-time algorithm that answers the following open problem: “given a string w over a fixed-sized alphabet, an integer k and a (regular or context-free) language L, decide whether there exists a string v∈ L such that w∼ kv.” The problem is NP-complete for a variable-sized alphabet.

Original languageEnglish
Title of host publicationDescriptional Complexity of Formal Systems - 24th IFIP WG 1.02 International Conference, DCFS 2022, Proceedings
EditorsYo-Sub Han, György Vaszil
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages15
ISBN (Print)9783031132568
Publication statusPublished - 2022
Event24th IFIP WG 1.02 International Conference on Descriptional Complexity of Formal Systems, DCFS 2022 - Debrecen, Hungary
Duration: 2022 Aug 292022 Aug 31

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume13439 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference24th IFIP WG 1.02 International Conference on Descriptional Complexity of Formal Systems, DCFS 2022

Bibliographical note

Funding Information:
Acknowledgments. We wish to thank the referees for letting us know related references and providing valuable suggestions that improve the presentation of the paper. This research was supported by the NRF grant funded by MIST (NRF-2020R1A4A3079947).

Publisher Copyright:
© 2022, IFIP International Federation for Information Processing.

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)


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