Characterization of lattice-valued multiset finite automata

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.