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12-11-2021 | Original Paper

Characterization of lattice-valued multiset finite automata

Authors: M. K. Dubey, Anand P. Singh, Mallika Dhingra

Published in: Granular Computing | Issue 4/2022

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Abstract

This work aims to characterize a new class of automaton with input as multisets. First, we introduce two finite monoids through different congruence relations on multiset associated with lattice-valued multiset finite automata and show that they are isomorphic to each other. Next, we present the quotient structure of lattice-valued multiset finite automata by defining an admissible relation on the set of states of a given lattice-valued multiset finite automata. Then we show that there is an isomorphism between lattice-valued multiset finite automata and the quotient structure of another lattice-valued multiset finite automata. Finally, we introduce the concept of reachability, observability (coreachability), and response maps of lattice-valued multiset finite recognizer. Interestingly, we show that the lattice-valued response map of a lattice-valued multiset finite recognizer leads us to provide a characterization of a lattice-valued multiset regular language.

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Title: Characterization of lattice-valued multiset finite automata
Authors: M. K. Dubey
Anand P. Singh
Mallika Dhingra
Publication date: 12-11-2021
Publisher: Springer International Publishing
Published in: Granular Computing / Issue 4/2022
Print ISSN: 2364-4966
Electronic ISSN: 2364-4974
DOI: https://doi.org/10.1007/s41066-021-00298-8

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