Dual Adjunction Between $Ω$-Automata and Wilke Algebra Quotients
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866929600039223296 |
|---|---|
| author | Chernev, Anton Hansen, Helle Hvid Kupke, Clemens |
| author_facet | Chernev, Anton Hansen, Helle Hvid Kupke, Clemens |
| contents | $Ω$-automata and Wilke algebras are formalisms for characterising $ω$-regular languages via their ultimately periodic words. $Ω$-automata read finite representations of ultimately periodic words, called lassos, and they are a subclass of lasso automata. We introduce lasso semigroups as a generalisation of Wilke algebras that mirrors how lasso automata generalise $Ω$-automata, and we show that finite lasso semigroups characterise regular lasso languages. We then show a dual adjunction between lasso automata and quotients of the free lasso semigroup with a recognising set, and as our main result we show that this dual adjunction restricts to one between $Ω$-automata and quotients of the free Wilke algebra with a recognising set. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_14115 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dual Adjunction Between $Ω$-Automata and Wilke Algebra Quotients Chernev, Anton Hansen, Helle Hvid Kupke, Clemens Formal Languages and Automata Theory $Ω$-automata and Wilke algebras are formalisms for characterising $ω$-regular languages via their ultimately periodic words. $Ω$-automata read finite representations of ultimately periodic words, called lassos, and they are a subclass of lasso automata. We introduce lasso semigroups as a generalisation of Wilke algebras that mirrors how lasso automata generalise $Ω$-automata, and we show that finite lasso semigroups characterise regular lasso languages. We then show a dual adjunction between lasso automata and quotients of the free lasso semigroup with a recognising set, and as our main result we show that this dual adjunction restricts to one between $Ω$-automata and quotients of the free Wilke algebra with a recognising set. |
| title | Dual Adjunction Between $Ω$-Automata and Wilke Algebra Quotients |
| topic | Formal Languages and Automata Theory |
| url | https://arxiv.org/abs/2407.14115 |