The generalized rank of trace languages

J 2019

The generalized rank of trace languages

KUNC, Michal and Jan MEITNER

Basic information

Original name

The generalized rank of trace languages

Authors

KUNC, Michal (203 Czech Republic, guarantor, belonging to the institution) and Jan MEITNER (203 Czech Republic, belonging to the institution)

Edition

International Journal of Foundations of Computer Science, Singapore, World Scientific Publishing Co Pte Ltd, 2019, 0129-0541

Other information

Language

English

Type of outcome

Článek v odborném periodiku

Field of Study

10101 Pure mathematics

Country of publisher

Singapore

Confidentiality degree

není předmětem státního či obchodního tajemství

References:

URL

Impact factor

Impact factor: 0.523

RIV identification code

RIV/00216224:14310/19:00107334

Organization unit

Faculty of Science

DOI

http://dx.doi.org/10.1142/S0129054119400070

UT WoS

000460314500008

Keywords in English

trace language; rank; regular language; rational series; tropical semiring

Abstract

V originále

Given a partially commutative alphabet and a set of words L, the rank of L expresses the amount of shuffling required to produce a word belonging to L from two words whose concatenation belongs to the closure of L with respect to the partial commutation. In this paper, the notion of rank is generalized from concatenations of two words to an arbitrary fixed number of words. In this way, an infinite sequence of non-negative integers and infinity is assigned to every set of words. It is proved that in the case of alphabets defining free commutative monoids, as well as in the more general case of direct products of free monoids, sequences of ranks of regular sets are exactly non-decreasing sequences that are eventually constant. On the other hand, by uncovering a relationship between rank sequences of regular sets and rational series over the min-plus semiring, it is shown that already for alphabets defining free products of free commutative monoids, rank sequences need not be eventually periodic.

Links

GA15-02862S, research and development project

Name: Aplikace algebry a kombinatoriky v teorii formálních jazyků

Investor: Czech Science Foundation

Citovat

KUNC, Michal and Jan MEITNER. The generalized rank of trace languages. International Journal of Foundations of Computer Science. Singapore: World Scientific Publishing Co Pte Ltd, 2019, vol. 30, No 1, p. 135-169. ISSN 0129-0541. Available from: https://dx.doi.org/10.1142/S0129054119400070.

@article{1513158,
   author = {Kunc, Michal and Meitner, Jan},
   article_location = {Singapore},
   article_number = {1},
   doi = {http://dx.doi.org/10.1142/S0129054119400070},
   keywords = {trace language; rank; regular language; rational series; tropical semiring},
   language = {eng},
   issn = {0129-0541},
   journal = {International Journal of Foundations of Computer Science},
   title = {The generalized rank of trace languages},
   url = {https://www.worldscientific.com/doi/10.1142/S0129054119400070},
   volume = {30},
   year = {2019}
}

TY  - JOUR
ID  - 1513158
AU  - Kunc, Michal - Meitner, Jan
PY  - 2019
TI  - The generalized rank of trace languages
JF  - International Journal of Foundations of Computer Science
VL  - 30
IS  - 1
SP  - 135-169
EP  - 135-169
PB  - World Scientific Publishing Co Pte Ltd
SN  - 01290541
KW  - trace language
KW  - rank
KW  - regular language
KW  - rational series
KW  - tropical semiring
UR  - https://www.worldscientific.com/doi/10.1142/S0129054119400070
L2  - https://www.worldscientific.com/doi/10.1142/S0129054119400070
N2  - Given a partially commutative alphabet and a set of words L, the rank of L expresses the amount of shuffling required to produce a word belonging to L from two words whose concatenation belongs to the closure of L with respect to the partial commutation. In this paper, the notion of rank is generalized from concatenations of two words to an arbitrary fixed number of words. In this way, an infinite sequence of non-negative integers and infinity is assigned to every set of words. It is proved that in the case of alphabets defining free commutative monoids, as well as in the more general case of direct products of free monoids, sequences of ranks of regular sets are exactly non-decreasing sequences that are eventually constant. On the other hand, by uncovering a relationship between rank sequences of regular sets and rational series over the min-plus semiring, it is shown that already for alphabets defining free products of free commutative monoids, rank sequences need not be eventually periodic.
ER  -

KUNC, Michal and Jan MEITNER. The generalized rank of trace languages. \textit{International Journal of Foundations of Computer Science}. Singapore: World Scientific Publishing Co Pte Ltd, 2019, vol.~30, No~1, p.~135-169. ISSN~0129-0541. Available from: https://dx.doi.org/10.1142/S0129054119400070.

Detailed Information on Publication Record