Finite Automata Over Infinite Alphabets: Two Models with Transitions for Local Change

  • Christopher Czyba
  • Christopher SpinrathEmail author
  • Wolfgang Thomas
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9168)


Two models of automata over infinite alphabets are presented, mainly with a focus on the alphabet \(\mathbb {N}\). In the first model, transitions can refer to logic formulas that connect properties of successive letters. In the second, the letters are considered as columns of a labeled grid which an automaton traverses column by column. Thus, both models focus on the comparison of successive letters, i.e. “local changes”. We prove closure (and non-closure) properties, show the decidability of the respective non-emptiness problems, prove limits on decidability results for extended models, and discuss open issues in the development of a generalized theory.


Finite Automaton Transition Formula Alphabet Letter Reachability Problem Alphabet Structure 
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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Christopher Czyba
    • 1
  • Christopher Spinrath
    • 1
    Email author
  • Wolfgang Thomas
    • 1
  1. 1.RWTH Aachen UniversityAachenGermany

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