Weighted Automata over Vector Spaces

In this paper we deal with three models of weighted automata that take weights in the field of real numbers. The first of these models are classical weighted finite automata, the second one are crisp-deterministic weighted automata, and the third one are weighted automata over a vector space. We explore the interrelationships between weighted automata over a vector space and other two models.Comment: In Proceedings AFL 2023, arXiv:2309.0112

Different models of automata with fuzzy states

In this paper we provide a general definition of automata with fuzzy stateswhich includes as its special cases automata used by Lin et al. [29], Liu and Qiu [30,31,42]and Xing et al. [56] in the study of fuzzy discrete event systems, as well as various typesof automata constructed in [14,15,18,32] for the purpose of the determinization of fuzzyautomata. We explain the relationships between these differentmodels of automata withfuzzy states and showthat every crisp-deterministic fuzzy automaton can be transformedinto a language-equivalent automaton with fuzzy states, and vice versa

A coalgebraic approach to fuzzy automata

In this thesis, we make a coalgebraic description of fuzzy automata allowing their integration in much general context. Thus, results obtained indivudually to fuzzy automata end up to be consequence of their coalgebraic description. In particular, a coalgebraic definition of the fuzzy language recognized by a fuzzy automaton is obtained. And, by defining a monad for fuzzy sets, a functor that describes a determinization process via a generalization of the powerset construction is obtained