The omega-reducibility of pseudovarieties of ordered monoids representing low levels of concatenation hierarchies

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F24%3A00139723" target="_blank" >RIV/00216224:14310/24:00139723 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.worldscientific.com/doi/full/10.1142/S0218196724500024?srsltid=AfmBOoq2CRwCpN5aKfIpF_TSlrx94zaKhBEXVq8tbD_fgeUJii51AOAh" target="_blank" >https://www.worldscientific.com/doi/full/10.1142/S0218196724500024?srsltid=AfmBOoq2CRwCpN5aKfIpF_TSlrx94zaKhBEXVq8tbD_fgeUJii51AOAh</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1142/S0218196724500024" target="_blank" >10.1142/S0218196724500024</a>

Jazyk výsledku

angličtina

Název v původním jazyce

The omega-reducibility of pseudovarieties of ordered monoids representing low levels of concatenation hierarchies

Popis výsledku v původním jazyce

We deal with the question of the omega-reducibility of pseudovarieties of ordered monoids corresponding to levels of concatenation hierarchies of regular languages. A pseudovariety of ordered monoids V is called omega-reducible if, given a finite ordered monoid M, for every inequality of pseudowords that is valid in V, there exists an inequality of omega-words that is also valid in V and has the same "imprint" in M.Place and Zeitoun have recently proven the decidability of the membership problem for levels 1/2, 1, 3/2 and 5/2 of concatenation hierarchies with level 0 being a finite Boolean algebra of regular languages closed under quotients. The solutions of these membership problems have been found by considering a more general problem of separation of regular languages and its further generalization - a problem of covering. Following the results of Place and Zeitoun, we prove that, for every concatenation hierarchy with level 0 being represented by a locally finite pseudovariety of monoids, the pseudovarieties corresponding to levels 1/2 and 3/2 are omega-reducible. As a corollary of these results, we obtain that, for every concatenation hierarchy with level 0 being represented by a locally finite pseudovariety of monoids, the pseudovarieties corresponding to levels 3/2 and 5/2 are definable by omega-inequalities. Furthermore, in the special case of the Straubing-Therien hierarchy, using a characterization theorem for level 2 by Place and Zeitoun, we obtain that the level 2 is definable by omega-identities.

Název v anglickém jazyce

The omega-reducibility of pseudovarieties of ordered monoids representing low levels of concatenation hierarchies

Popis výsledku anglicky

We deal with the question of the omega-reducibility of pseudovarieties of ordered monoids corresponding to levels of concatenation hierarchies of regular languages. A pseudovariety of ordered monoids V is called omega-reducible if, given a finite ordered monoid M, for every inequality of pseudowords that is valid in V, there exists an inequality of omega-words that is also valid in V and has the same "imprint" in M.Place and Zeitoun have recently proven the decidability of the membership problem for levels 1/2, 1, 3/2 and 5/2 of concatenation hierarchies with level 0 being a finite Boolean algebra of regular languages closed under quotients. The solutions of these membership problems have been found by considering a more general problem of separation of regular languages and its further generalization - a problem of covering. Following the results of Place and Zeitoun, we prove that, for every concatenation hierarchy with level 0 being represented by a locally finite pseudovariety of monoids, the pseudovarieties corresponding to levels 1/2 and 3/2 are omega-reducible. As a corollary of these results, we obtain that, for every concatenation hierarchy with level 0 being represented by a locally finite pseudovariety of monoids, the pseudovarieties corresponding to levels 3/2 and 5/2 are definable by omega-inequalities. Furthermore, in the special case of the Straubing-Therien hierarchy, using a characterization theorem for level 2 by Place and Zeitoun, we obtain that the level 2 is definable by omega-identities.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10100 - Mathematics

Projekt

<a href="/cs/project/GA19-12790S" target="_blank" >GA19-12790S: Efektivní charakterizace tříd konečných pologrup a formálních jazyků</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2024

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

International Journal of Algebra and Computation

ISSN

0218-1967

e-ISSN

1793-6500

Svazek periodika

34

Číslo periodika v rámci svazku

01

Stát vydavatele periodika

SG - Singapurská republika

Počet stran výsledku

49

Strana od-do

87-135

Kód UT WoS článku

001179257000004

EID výsledku v databázi Scopus

2-s2.0-85187575125