Abstract
The paper investigates the state complexity of two operations on regular languages, known as GF(2)-concatenation and GF(2)-inverse (Bakinova et al., “Formal languages over GF(2)”, LATA 2018), in the case of a one-symbol alphabet. The GF(2)-concatenation is a variant of the classical concatenation obtained by replacing Boolean logic in its definition with the GF(2) field; it is proved that GF(2)-concatenation of two unary languages recognized by an m-state and an n-state DFA is recognized by a DFA with 2mn states, and this number of states is necessary in the worst case, as long as m and n are relatively prime. This operation is known to have an inverse, and the state complexity of the GF(2)-inverse operation over a unary alphabet is proved to be exactly 2n−1 + 1.
| Original language | English |
|---|---|
| Title of host publication | Descriptional Complexity of Formal Systems - 21st IFIP WG 1.02 International Conference, DCFS 2019, Proceedings |
| Editors | Stavros Konstantinidis, Michal Hospodár, Galina Jirásková |
| Publisher | Springer |
| Pages | 248-259 |
| Number of pages | 12 |
| ISBN (Print) | 9783030232467 |
| DOIs | |
| Publication status | Published - 1 Jul 2019 |
| Event | 21st International Conference on Descriptional Complexity of Formal Systems, DCFS 2019 - Košice Duration: 17 Jul 2019 → 19 Jul 2019 |
Publication series
| Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
|---|---|
| Volume | 11612 LNCS |
| ISSN (Print) | 0302-9743 |
| ISSN (Electronic) | 1611-3349 |
Conference
| Conference | 21st International Conference on Descriptional Complexity of Formal Systems, DCFS 2019 |
|---|---|
| Country | Slovakia |
| City | Košice |
| Period | 17/07/19 → 19/07/19 |
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Scopus subject areas
- Theoretical Computer Science
- Computer Science(all)
Cite this
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State Complexity of GF(2)-Concatenation and GF(2)-Inverse on Unary Languages. / Okhotin, Alexander; Sazhneva, Elizaveta.
Descriptional Complexity of Formal Systems - 21st IFIP WG 1.02 International Conference, DCFS 2019, Proceedings. ed. / Stavros Konstantinidis; Michal Hospodár; Galina Jirásková. Springer, 2019. p. 248-259 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11612 LNCS).Research output › › peer-review
TY - GEN
T1 - State Complexity of GF(2)-Concatenation and GF(2)-Inverse on Unary Languages
AU - Okhotin, Alexander
AU - Sazhneva, Elizaveta
PY - 2019/7/1
Y1 - 2019/7/1
N2 - The paper investigates the state complexity of two operations on regular languages, known as GF(2)-concatenation and GF(2)-inverse (Bakinova et al., “Formal languages over GF(2)”, LATA 2018), in the case of a one-symbol alphabet. The GF(2)-concatenation is a variant of the classical concatenation obtained by replacing Boolean logic in its definition with the GF(2) field; it is proved that GF(2)-concatenation of two unary languages recognized by an m-state and an n-state DFA is recognized by a DFA with 2mn states, and this number of states is necessary in the worst case, as long as m and n are relatively prime. This operation is known to have an inverse, and the state complexity of the GF(2)-inverse operation over a unary alphabet is proved to be exactly 2n−1 + 1.
AB - The paper investigates the state complexity of two operations on regular languages, known as GF(2)-concatenation and GF(2)-inverse (Bakinova et al., “Formal languages over GF(2)”, LATA 2018), in the case of a one-symbol alphabet. The GF(2)-concatenation is a variant of the classical concatenation obtained by replacing Boolean logic in its definition with the GF(2) field; it is proved that GF(2)-concatenation of two unary languages recognized by an m-state and an n-state DFA is recognized by a DFA with 2mn states, and this number of states is necessary in the worst case, as long as m and n are relatively prime. This operation is known to have an inverse, and the state complexity of the GF(2)-inverse operation over a unary alphabet is proved to be exactly 2n−1 + 1.
UR - http://www.scopus.com/inward/record.url?scp=85069478114&partnerID=8YFLogxK
U2 - 10.1007/978-3-030-23247-4_19
DO - 10.1007/978-3-030-23247-4_19
M3 - Conference contribution
AN - SCOPUS:85069478114
SN - 9783030232467
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 248
EP - 259
BT - Descriptional Complexity of Formal Systems - 21st IFIP WG 1.02 International Conference, DCFS 2019, Proceedings
A2 - Konstantinidis, Stavros
A2 - Hospodár, Michal
A2 - Jirásková, Galina
PB - Springer
ER -