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

Fuzzy Automata: A Quantitative Review

Classical automata theory cannot deal with the system uncertainty. To deal with the system uncertainty the concept of fuzzy finite automata was proposed. Fuzzy automata can be used in diverse applications such as fault detection, pattern matching, measuring the fuzziness between strings, description of natural languages, neural network, lexical analysis, image processing, scheduling problem and many more. In this paper, a methodical literature review is carried out on various research works in the field of Fuzzy automata and explained the challenging issues in the field of fuzzy automata

Poboljšani algoritmi za determinizaciju fazi i težinskih automata

Determinization algorithms are methods that calculate complete deterministic fuzzy (weighted) automaton that is language equivalent to the input fuzzy (weighted) automaton, and they have found application in numerous fields, including lexicographic analysis, analysis of regular expressions, automatic speech recognition, pattern recognition in artificial intelligence, etc. Especially important class of determinization algorithms are canonization algorithms, which produce minimal complete deterministic fuzzy (weighted) automaton equivalent to the input fuzzy (weighted) automaton. The aim of this dissertation is the development of determinization algorithms based on the concept of factorizations, as well as computing and merging of the indistinguishable states of fuzzy (weighted) automaton under construction. At the same time, computing and merging of the indistinguishable states is done by right and left invariant fuzzy relations in the case of fuzzy automata, as well as by right and left invariant Boolean matrices in the case of weighted automata. We apply the partition refinement technique to obtain improved algorithms for computing the greatest right and left invariant Boolean equivalence and quasi – order matrices. In the end, we consider ways to compute the greatest right and left invariant fuzzy equivalences and fuzzy quasi – orders when the algorithms for their computation, based on the partition refinement technique, are unable to stop in a finite number of steps