| Issue |
RAIRO-Theor. Inf. Appl.
Volume 57, 2023
12th International Workshop on Non-Classical Models of Automata and Applications (NCMA 2022)
|
|
|---|---|---|
| Article Number | 9 | |
| Number of page(s) | 20 | |
| DOI | https://doi.org/10.1051/ita/2023010 | |
| Published online | 07 November 2023 | |
On the accepting state complexity of operations on permutation automata
Institut für Informatik, Universität Giessen, Arndtstr. 2, 35392 Giessen, Germany
* Corresponding author: christian.rauch@informatik.uni-giessen.de
Received:
30
January
2023
Accepted:
19
September
2023
We investigate the accepting state complexity of deterministic finite automata for regular languages obtained by applying one of the following operations on languages accepted by permutation automata: union, quotient, complement, difference, intersection, Kleene star, Kleene plus, and reversal. The paper thus joins the study of the accepting state complexity of regularity preserving language operations which was initiated in [J. Dassow, J. Autom., Lang. Comb. 21 (2016) 55–67]. We show that for almost all of the above-mentioned operations, except for reversal and quotient, there is no difference in the accepting state complexity for permutation automata compared to deterministic finite automata in general. For both reversal and quotient we prove that certain accepting state complexities cannot be obtained; these numbers are called “magic” in the literature. Moreover, we solve the left open accepting state complexity problem for the intersection of unary languages accepted by permutation automata and deterministic finite automata in general.
Mathematics Subject Classification: 68Q04 / 68Q10 / 68Q45
Key words: Permutation automata / language operations / accepting state complexity / descriptional complexity
© The authors. Published by EDP Sciences, 2023
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