We introduce and study a new class of automata able to consume and produce multisets; we call them Mealy multiset automata. We are interested in their algebraic and coalgebraic properties. After some useful properties of multisets, we present the notions of bisimulation, observability, and behavior for Mealy multiset automata. We give a characterization of the bisimulation between two Mealy multiset automata, and a result relating their general behavior to their sequential behavior. We describe an endofunctor of the category of Set such that a Mealy multiset automaton is a coalgebra of this functor. This functor preserves coproducts, coequalizers, and weak pullbacks. Moreover, the new defined bisimulation is an instance of a more general coalgebraic definition.
['Gabriel Ciobanu', 'Viorel Mihai Gontineac']
Algebraic and coalgebraic aspects of membrane computing