l-Valued multiset automata and l-valued multiset languages

2020 ◽  
pp. 1-15
Author(s):  
Vinay Gautam
Keyword(s):  
Finite Automaton ◽  
Residuated Lattice ◽  
Regular Languages ◽  
Automata Theory ◽  
Necessary And Sufficient Condition ◽  
Zero Divisors ◽  
Complete Residuated Lattice ◽  
Pumping Lemma ◽  
Deterministic Formula ◽  
Necessary And Sufficient

The reason for this work is to present and study deterministic multiset automata, multiset automata and their languages with membership values in complete residuated lattice without zero divisors. We build up the comparability of deterministic [Formula: see text]-valued multiset finite automaton and [Formula: see text]-valued multiset finite automaton in sense of recognizability of a [Formula: see text]-valued multiset language. Then, we relate multiset regular languages to a given [Formula: see text]-valued multiset regular languages and vice versa. At last, we present the concept of pumping lemma for [Formula: see text]-valued multiset automata theory, which we utilize to give a necessary and sufficient condition for a [Formula: see text]-valued multiset language to be non-constant.

Fuzzy Regular Languages Based on Residuated Lattice

2020 ◽  
Vol 16 (02) ◽  
pp. 363-376
Author(s):  
Anupam K. Singh ◽  
S. P. Tiwari
Keyword(s):  
Residuated Lattice ◽  
Finite Automata ◽  
Regular Languages ◽  
Sufficient Condition ◽  
Membership Functions ◽  
Necessary And Sufficient Condition ◽  
Complete Residuated Lattice ◽  
Pumping Lemma ◽  
Fuzzy Finite Automata ◽  
Necessary And Sufficient

The purpose of this work is to introduce the concept of fuzzy regular languages (FRL) accepted by fuzzy finite automata, and try to introduce the categorical look of fuzzy languages where the codomain of membership functions are taken as a complete residuated lattice, instead of [Formula: see text]. Also, we have introduced pumping lemma for FRL, which is used to establish a necessary and sufficient condition for a given fuzzy languages to be non-constant.

scholarly journals Injective and projective semimodules over involutive semirings

2021 ◽  
pp. 2250182
Author(s):  
Peter Jipsen ◽  
Sara Vannucci
Keyword(s):  
Crucial Role ◽  
Residuated Lattice ◽  
Residuated Lattices ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Term Equivalence ◽  
Involutive Residuated Lattice ◽  
Necessary And Sufficient ◽  
Mv Algebras

We show that the term equivalence between MV-algebras and MV-semirings lifts to involutive residuated lattices and a class of semirings called involutive semirings. The semiring perspective leads to a necessary and sufficient condition for the interval [Formula: see text] to be a subalgebra of an involutive residuated lattice, where [Formula: see text] is the dualizing element. We also import some results and techniques of semimodule theory in the study of this class of semirings, generalizing results about injective and projective MV-semimodules. Indeed, we note that the involution plays a crucial role and that the results for MV-semirings are still true for involutive semirings whenever the Mundici functor is not involved. In particular, we prove that involution is a necessary and sufficient condition in order for projective and injective semimodules to coincide.

scholarly journals On rational solution of the state equation of a finite automaton

1988 ◽  
Vol 11 (2) ◽  
pp. 355-364
Author(s):  
R. Chaudhuri ◽  
H. Höft
Keyword(s):  
Finite Automaton ◽  
Rational Solution ◽  
State Equation ◽  
The State ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient

We prove that the necessary and sufficient condition for the state equation of a finite automatonMto have a rational solution is that the lexicographical Gödel numbers of the strings belonging to each of the end-sets ofMform an ultimately periodic set. A method of determining the existence of a rational solution of the state equation is also given.

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