Characterization of Ordered Semigroups Generating Well
Quasi-Orders of Words

J 2024

Characterization of Ordered Semigroups Generating Well Quasi-Orders of Words

KLÍMA, Ondřej and Jonatan KOLEGAR

Basic information

Original name

Characterization of Ordered Semigroups Generating Well Quasi-Orders of Words

Authors

KLÍMA, Ondřej (203 Czech Republic, belonging to the institution) and Jonatan KOLEGAR (203 Czech Republic, belonging to the institution)

Edition

Theory of Computing Systems, New York, Springer, 2024, 1432-4350

Other information

Language

English

Type of outcome

Článek v odborném periodiku

Field of Study

10101 Pure mathematics

Country of publisher

United States of America

Confidentiality degree

není předmětem státního či obchodního tajemství

References:

URL

Impact factor

Impact factor: 0.500 in 2022

Organization unit

Faculty of Science

DOI

http://dx.doi.org/10.1007/s00224-024-10172-0

UT WoS

001200343100001

Keywords in English

Finite semigroups; Well quasi-orders; Unavoidable words; Derivation relations; Ordered semigroups

Abstract

V originále

The notion of a quasi-order generated by a homomorphism from the semigroup of all words onto a finite ordered semigroup was introduced by Bucher et al. (Theor. Comput. Sci. 40, 131-148 1985). It naturally occurred in their studies of derivation relations associated with a given set of context-free rules, and they asked a crucial question, whether the resulting relation is a well quasi-order. We answer this question in the case of the quasi-order generated by a semigroup homomorphism. We show that the answer does not depend on the homomorphism, but it is a property of its image. Moreover, we give an algebraic characterization of those finite semigroups for which we get well quasi-orders. This characterization completes the structural characterization given by Kunc (Theor. Comput. Sci. 348, 277-293 2005) in the case of semigroups ordered by equality. Compared with Kunc's characterization, the new one has no structural meaning, and we explain why that is so. In addition, we prove that the new condition is testable in polynomial time.

Links

GA19-12790S, research and development project

Name: Efektivní charakterizace tříd konečných pologrup a formálních jazyků

Investor: Czech Science Foundation

Citovat

KLÍMA, Ondřej and Jonatan KOLEGAR. Characterization of Ordered Semigroups Generating Well Quasi-Orders of Words. Theory of Computing Systems. New York: Springer, 2024, vol. 68, No 3, p. 380-402. ISSN 1432-4350. Available from: https://dx.doi.org/10.1007/s00224-024-10172-0.

@article{2420579,
   author = {Klíma, Ondřej and Kolegar, Jonatan},
   article_location = {New York},
   article_number = {3},
   doi = {http://dx.doi.org/10.1007/s00224-024-10172-0},
   keywords = {Finite semigroups; Well quasi-orders; Unavoidable words; Derivation relations; Ordered semigroups},
   language = {eng},
   issn = {1432-4350},
   journal = {Theory of Computing Systems},
   title = {Characterization of Ordered Semigroups Generating Well Quasi-Orders of Words},
   url = {https://link.springer.com/article/10.1007/s00224-024-10172-0},
   volume = {68},
   year = {2024}
}

TY  - JOUR
ID  - 2420579
AU  - Klíma, Ondřej - Kolegar, Jonatan
PY  - 2024
TI  - Characterization of Ordered Semigroups Generating Well Quasi-Orders of Words
JF  - Theory of Computing Systems
VL  - 68
IS  - 3
SP  - 380-402
EP  - 380-402
PB  - Springer
SN  - 14324350
KW  - Finite semigroups
KW  - Well quasi-orders
KW  - Unavoidable words
KW  - Derivation relations
KW  - Ordered semigroups
UR  - https://link.springer.com/article/10.1007/s00224-024-10172-0
N2  - The notion of a quasi-order generated by a homomorphism from the semigroup of all words onto a finite ordered semigroup was introduced by Bucher et al. (Theor. Comput. Sci. 40, 131-148 1985). It naturally occurred in their studies of derivation relations associated with a given set of context-free rules, and they asked a crucial question, whether the resulting relation is a well quasi-order. We answer this question in the case of the quasi-order generated by a semigroup homomorphism. We show that the answer does not depend on the homomorphism, but it is a property of its image. Moreover, we give an algebraic characterization of those finite semigroups for which we get well quasi-orders. This characterization completes the structural characterization given by Kunc (Theor. Comput. Sci. 348, 277-293 2005) in the case of semigroups ordered by equality. Compared with Kunc's characterization, the new one has no structural meaning, and we explain why that is so. In addition, we prove that the new condition is testable in polynomial time.
ER  -

KLÍMA, Ondřej and Jonatan KOLEGAR. Characterization of Ordered Semigroups Generating Well Quasi-Orders of Words. \textit{Theory of Computing Systems}. New York: Springer, 2024, vol.~68, No~3, p.~380-402. ISSN~1432-4350. Available from: https://dx.doi.org/10.1007/s00224-024-10172-0.

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