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We show that a special case of the Feferman-Vaught composition theorem givesrise to a natural notion of automata for finite words over an infinitealphabet, with good closure and decidability properties, as well as severallogical characterizations. We also consider a slight extension of theFeferman-Vaught formalism which allows to express more relations betweencomponent values (such as equality), and prove related decidability results.  From this result we get new classes of decidable logics for words over aninfinite alphabet.

An Application of the Feferman-Vaught Theorem to Automata and Logics for Words over an Infinite Alphabet

An Application of the Feferman-Vaught Theorem to Automata and Logics for
Words over an Infinite Alphabet