Diekert Volker and Walter Tobias: Asymptotic approximation for the quotient complexities of atoms. In: Acta cybernetica, (22) 2. pp. 349-357. (2015)
Preview |
Cikk, tanulmány, mű
actacyb_22_2_2015_7.pdf Download (343kB) | Preview |
Abstract
In a series of papers, Brzozowski together with Tamm, Davies, and Szykuła studied the quotient complexities of atoms of regular languages [6, 7, 3, 4]. The authors obtained precise bounds in terms of binomial sums for the most complex situations in the following five cases: (G): general, (R): right ideals, (L): left ideals, (T): two-sided ideals and (S): suffix-free languages. In each case let κc(n) be the maximal complexity of an atom of a regular language L, where L has complexity n ≥ 2 and belongs to the class C ϵ {G, R, L, T , S}. It is known that κT(n) ≤ κL(n) = κR(n) ≤ κG(n) < 3n and κS(n) = κL(n−1). We show that the ratio κC(n)/κC(n−1) tends exponentially fast to 3 in all five cases but it remains different from 3. This behaviour was suggested by experimental results of Brzozowski and Tamm; and the result for G was shown independently by Luke Schaeffer and the first author soon after the paper of Brzozowski and Tamm appeared in 2012. However, proofs for the asymptotic behavior of κG(n)/κG(n−1) were never published; and the results here are valid for all five classes above. Moreover, there is an interesting oscillation for all C: for almost all n we have κC(n)/κC(n−1) > 3 if and only if κC(n+1)/κC(n) < 3.
| Item Type: | Article |
|---|---|
| Journal or Publication Title: | Acta cybernetica |
| Date: | 2015 |
| Volume: | 22 |
| Number: | 2 |
| ISSN: | 0324-721X |
| Page Range: | pp. 349-357 |
| Language: | English |
| Place of Publication: | Szeged |
| Related URLs: | http://acta.bibl.u-szeged.hu/38540/ |
| DOI: | 10.14232/actacyb.22.2.2015.7 |
| Uncontrolled Keywords: | Reakcióképesség - kémiai |
| Additional Information: | Bibliogr.: p. 356-357. ; összefoglalás angol nyelven |
| Subjects: | 01. Natural sciences 01. Natural sciences > 01.02. Computer and information sciences |
| Date Deposited: | 2016. Oct. 17. 10:36 |
| Last Modified: | 2022. Jun. 20. 09:55 |
| URI: | http://acta.bibl.u-szeged.hu/id/eprint/36117 |
Actions (login required)
 |
View Item |
