On minimal realization for a fuzzy language and Brzozowski’s algorithm

Tiwari, S. P.; Gautam, Vinay; Davvaz, Bijan

doi:10.3233/ifs-151673

Cited by 20 publications

(7 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this section we recall some concepts related to multiset automata which we need for completeness of the paper. ese concepts can be found in [54,55,58,64,78].…”

Section: Multiset Automatamentioning

confidence: 99%

“…De nition 9. [54,55,58,64,78] A multiset automaton (MA) is a 5-tuple M (Q, Σ, δ, q 0 , F), where (i) Q and Σ are nonempty sets called the state-set and input-set, respectively;…”

Section: Multiset Automatamentioning

confidence: 99%

“…[57]). e deterministic fuzzy multiset finite automata and fuzzy multiset finite automata have been shown equivalent potential in terms of acceptance of a fuzzy multiset language by Tiwari et al [58] and in addition minimal realization of a fuzzy multiset language have also been studied by them through the right congruence relation.…”

Section: Introductionmentioning

confidence: 99%

“…e minimization problem of fuzzy multiset automata and fuzzy multiset languages having membership values in distributive lattices have been studied by Tiwari et al [58], using the right congruence relation, a key concept of Myhill-Nerode theory, and concept of derivative of a fuzzy multiset language. Wang and Li [64] also studied the minimization problem using the right congruence relation defined on the state-set of deterministic lattice multiset automata and presented an efficient minimization algorithm where unreachable states were removed in the process of minimization.…”

Section: Introductionmentioning

confidence: 99%

“…(ii) the minimal realization for given fuzzy multiset languages and minimization of fuzzy multiset automata studied so for uses (i) concept of Myhill-Nerode equivalence relation defined either on input multiset [58,64], or through defining equivalence relation on state set of deterministic lattice valued multiset automata and removal of unreachable states [64], (ii) derivative of fuzzy languages [58], (iii) Brzozowski's minimization algorithm [78]; (iii) except Pal and Tiwari [78], no work has been reported for studying fuzzy multiset automata and fuzzy multiset languages via categorical concept; while, the categorical approach has been shown to be helpful in the study of several aspects of classical automata and languages, as well as fuzzy automata and fuzzy languages, as mentioned above.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

A General Categorical Framework of Minimal Realization Theory for a Fuzzy Multiset Language

Yadav

Tiwari

2022

Mathematical Problems in Engineering

View full text Add to dashboard Cite

This paper is to study the minimal realization theory for a fuzzy multiset language in the framework of category theory, which has already provided the tools and techniques for the advancement of several features of theoretical computer science. Specifically, by using the well-known categorical concepts, it is shown herein that there is a minimal realization (called the Nerode realization) for each fuzzy multiset language, and all minimal realizations for a given fuzzy multiset language are isomorphic to it.

show abstract

“…In this section we recall some concepts related to multiset automata which we need for completeness of the paper. ese concepts can be found in [54,55,58,64,78].…”

Section: Multiset Automatamentioning

confidence: 99%

“…De nition 9. [54,55,58,64,78] A multiset automaton (MA) is a 5-tuple M (Q, Σ, δ, q 0 , F), where (i) Q and Σ are nonempty sets called the state-set and input-set, respectively;…”

Section: Multiset Automatamentioning

confidence: 99%