Pumping lemma in automata theory based on complete residuated lattice-valued logic: A note

2006 ◽  
Vol 157 (15) ◽  
pp. 2128-2138 ◽  
Author(s):  
Daowen Qiu
Keyword(s):  
Residuated Lattice ◽  
Automata Theory ◽  
Complete Residuated Lattice ◽  
Pumping Lemma

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.

Equivalence in automata theory based on complete residuated lattice-valued logic

2007 ◽  
Vol 158 (13) ◽  
pp. 1407-1422 ◽  
Author(s):  
Hongyan Xing ◽  
Daowen Qiu ◽  
Fuchun Liu ◽  
Zhujun Fan
Keyword(s):  
Residuated Lattice ◽  
Automata Theory ◽  
Complete Residuated Lattice
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