Using Multiplicity Automata to Identify Transducer Relations from Membership and Equivalence Queries ## AbstractMultiplicity Automata are devices that implement functions from a string space to a field. Usually the real number’s field is used. From a learning point of view there exists some algorithms that are able to identify any multiplicity automaton from membership and equivalence queries. In this work we realize that those algorithms can also be used if the algebraic structure of a field is relaxed to a divisive ring structure, that is, the commutativity of the product operation is dropped. Moreover, we define an algebraic structure, which is an extension of the string monoid, that allows the identification of any transduction that can be realized by finite state machines without empty-transitions.
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