scholarly journals Algebraic Properties of Intuitionistic L-fuzzy Multiset Finite Automata

2021 ◽  
Author(s):  
Yongbing Wang ◽  
Lixia Zhang
Keyword(s):  
Finite Automata ◽  
Transformation Semigroup ◽  
Bijective Correspondence ◽  
Finite Monoids ◽  
Algebraic Properties ◽  
Congruence Relations

Abstract Algrbraic properties and structures of intuitionistic L -fuzzy multiset finite automata (ILFMA) are discussed through congruences on a semigroup in this paper. Firstly,we put forward the notion of the intuitionistic L -fuzzy compatible relation, the compatible monoid associated to the intuitionistic L- fuzzy compatible relation can be effectively constructed, and we construct two finite monoids through two different congruence relations on a given ILFMA, then we also prove that they are isomorphic. Furthermore, using the quotient structure of ILFMA, algebraic properties of intuitionistic L -fuzzy multiset transformation semigroup are discussed. According to intuitionistic L -admissible relation and homomorphism of ILFMA, we show that there is a bijective correspondence between an ILFMA and the quotient structure of another ILFMA.

THE ORBIT STRUCTURE OF FINITE MONOIDS

1993 ◽  
Vol 03 (04) ◽  
pp. 557-573 ◽  
Author(s):  
ROB CARSCADDEN
Keyword(s):  
Transformation Semigroup ◽  
Unit Group ◽  
Full Transformation ◽  
Finite Monoid ◽  
Orbit Structure ◽  
Finite Monoids ◽  
Full Transformation Semigroup ◽  
Green’S Relation

Let M be a finite monoid with unit group G. We consider a refinement, [Formula: see text] of the Green’s relation [Formula: see text]. The [Formula: see text]-classes, denoted [Formula: see text] are the G×G orbits, GHG, of the ℋ-classes, H, of M. With an orbit [Formula: see text] we associate a local monoid [Formula: see text] and determine the structure of these local monoids. The theory is applied to the full transformation semigroup [Formula: see text] and we see that the number of orbits [Formula: see text] in [Formula: see text] is equal to the number of partitions of n.

Algebraic properties of L-fuzzy finite automata

2013 ◽  
Vol 234 ◽  
pp. 182-202 ◽  
Author(s):  
Jianhua Jin ◽  
Qingguo Li ◽  
Yongming Li
Keyword(s):  
Finite Automata ◽  
Algebraic Properties ◽  
Fuzzy Finite Automata

scholarly journals Groups and semigroups defined by colorings of synchronizing automata

2014 ◽  
Vol 24 (06) ◽  
pp. 773-793 ◽  
Author(s):  
Daniele D'Angeli ◽  
Emanuele Rodaro
Keyword(s):  
Finite Automata ◽  
Deterministic Finite Automata ◽  
Combinatorial Properties ◽  
Automata Groups ◽  
Synchronizing Automata ◽  
Algebraic Properties ◽  
Mealy Automata ◽  
Group A ◽  
Free Semigroups ◽  
Self Similar

In this paper we combine the algebraic properties of Mealy machines generating self-similar groups and the combinatorial properties of the corresponding deterministic finite automata (DFA). In particular, we relate bounded automata to finitely generated synchronizing automata and characterize finite automata groups in terms of nilpotency of the corresponding DFA. Moreover, we present a decidable sufficient condition to have free semigroups in an automaton group. A series of examples and applications is widely discussed, in particular we show a way to color the de Bruijn automata into Mealy automata whose associated semigroups are free, and we present some structural results related to the associated groups.

scholarly journals Compatible Deductive Systems of Pulexes

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Shokoofeh Ghorbani
Keyword(s):  
Congruence Relation ◽  
Deductive System ◽  
Quotient Algebra ◽  
Bijective Correspondence ◽  
Deductive Systems ◽  
Congruence Relations

The notion of (compatible) deductive system of a pulex is defined and some properties of deductive systems are investigated. We also define a congruence relation on a pulex and show that there is a bijective correspondence between the compatible deductive systems and the congruence relations. We define the quotient algebra induced by a compatible deductive system and study its properties.

scholarly journals Formations of finite monoids and formal languages: Eilenberg's variety theorem revisited

2014 ◽  
Vol 26 (6) ◽  
Author(s):  
Adolfo Ballester-Bolinches ◽  
Jean-Éric Pin ◽  
Xaro Soler-Escrivà
Keyword(s):  
Formal Languages ◽  
Bijective Correspondence ◽  
Original Theory ◽  
Finite Monoids

AbstractWe present an extension of Eilenberg's variety theorem, a well-known result connecting algebra to formal languages. We prove that there is a bijective correspondence between formations of finite monoids and certain classes of languages, the formations of languages. Our result permits to treat classes of finite monoids which are not necessarily closed under taking submonoids, contrary to the original theory. We also prove a similar result for ordered monoids.

A novel cryptosystem based on abstract automata and Latin cubes

2015 ◽  
Vol 52 (2) ◽  
pp. 221-232
Author(s):  
Pál Dömösi ◽  
Géza Horváth
Keyword(s):  
Block Cipher ◽  
Finite Automata ◽  
Theoretical Background ◽  
Point Of View ◽  
Theoretical Point ◽  
Transition Matrices ◽  
Encryption And Decryption ◽  
Secret Keys ◽  
Automata Network ◽  
Fully Functioning

In this paper we introduce a novel block cipher based on the composition of abstract finite automata and Latin cubes. For information encryption and decryption the apparatus uses the same secret keys, which consist of key-automata based on composition of abstract finite automata such that the transition matrices of the component automata form Latin cubes. The aim of the paper is to show the essence of our algorithms not only for specialists working in compositions of abstract automata but also for all researchers interested in cryptosystems. Therefore, automata theoretical background of our results is not emphasized. The introduced cryptosystem is important also from a theoretical point of view, because it is the first fully functioning block cipher based on automata network.

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