A carregar...
Publicação
Tropical representations and identities of the stylic monoid
| Nome: | Descrição: | Tamanho: | Formato: | |
|---|---|---|---|---|
| 401.11 KB | Adobe PDF |
Autores
Orientador(es)
Resumo(s)
We exhibit a faithful representation of the stylic monoid of every finite rank as a monoid of upper unitriangular matrices over the tropical semiring. Thus, we show that the stylic monoid of finite rank n generates the pseudovariety Jn, which corresponds to the class of all piecewise testable languages of height n, in the framework of Eilenberg’s correspondence. From this, we obtain the equational theory of the stylic monoids of finite rank, show that they are finitely based if and only if n≤ 3 , and that their identity checking problem is decidable in linearithmic time. We also establish connections between the stylic monoids and other plactic-like monoids, and solve the finite basis problem for the stylic monoid with involution.
Descrição
Publisher Copyright:
© 2022, The Author(s).
Palavras-chave
Finite basis problem Involution Monoid identities Stylic monoid Tropical representation Unitriangular matrices Algebra and Number Theory