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The paper "Symbolic Finite State Transducers, Algorithms and Applications" by Bjorner et al (to appear at POPL 2012) describes one type of finite-state, infinite-alphabet automata/transducers by using predicates from any decidable theory as the alphabet. The paper also references quite a few others including:

  • "Automata and logics for words and trees over an infinite alphabet" by Segoufin,
  • "Finite memory automata" by Kaminski and Francez, FOCS 1990

I'm wondering whether there's a good survey on different infinite alphabet automata models.

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    $\begingroup$ I recently read Bojanczyk et al. "Automata with Group Actions," and it cites Segoufin as the survey of this area. $\endgroup$ – Radu GRIGore Oct 28 '11 at 20:22

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