On Transition Constructions for Automata -- A Categorical Perspective

Fuente: arXiv
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Auteur principal: Cruchten, Mike
Format: Preprint
Publié: 2024
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author Cruchten, Mike
author_facet Cruchten, Mike
contents We investigate the transition monoid construction for deterministic automata in a categorical setting and establish it as an adjunction. We pair this adjunction with two other adjunctions to obtain two endofunctors on deterministic automata, a comonad and a monad, which are closely related, respectively, to the largest set of equations and the smallest set of coequations satisfied by an automaton. Furthermore, we give similar transition algebra constructions for lasso and Ω-automata, and show that they form adjunctions. We present some initial results on sets of equations and coequations for lasso automata.
format Preprint
id arxiv_https___arxiv_org_abs_2406_19312
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle On Transition Constructions for Automata -- A Categorical Perspective
Cruchten, Mike
Formal Languages and Automata Theory
68Q45
F.4.3; F.1.1
We investigate the transition monoid construction for deterministic automata in a categorical setting and establish it as an adjunction. We pair this adjunction with two other adjunctions to obtain two endofunctors on deterministic automata, a comonad and a monad, which are closely related, respectively, to the largest set of equations and the smallest set of coequations satisfied by an automaton. Furthermore, we give similar transition algebra constructions for lasso and Ω-automata, and show that they form adjunctions. We present some initial results on sets of equations and coequations for lasso automata.
title On Transition Constructions for Automata -- A Categorical Perspective
topic Formal Languages and Automata Theory
68Q45
F.4.3; F.1.1
url https://arxiv.org/abs/2406.19312