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.
|Title of host publication||Descriptional Complexity of Formal Systems - 24th IFIP WG 1.02 International Conference, DCFS 2022, Proceedings|
|Editors||Yo-Sub Han, György Vaszil|
|Publisher||Springer Science and Business Media Deutschland GmbH|
|Number of pages||15|
|Publication status||Published - 2022|
|Event||24th IFIP WG 1.02 International Conference on Descriptional Complexity of Formal Systems, DCFS 2022 - Debrecen, Hungary|
Duration: 2022 Aug 29 → 2022 Aug 31
|Name||Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)|
|Conference||24th IFIP WG 1.02 International Conference on Descriptional Complexity of Formal Systems, DCFS 2022|
|Period||22/8/29 → 22/8/31|
Bibliographical noteFunding 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).
© 2022, IFIP International Federation for Information Processing.
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Computer Science(all)