Nominal Automata with Name Binding

  • Lutz SchröderEmail author
  • Dexter Kozen
  • Stefan Milius
  • Thorsten Wißmann
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10203)


Nominal sets are a convenient setting for languages over infinite alphabets, i.e. data languages. We introduce an automaton model over nominal sets, regular nondeterministic nominal automata (RNNA), which have a natural coalgebraic definition using abstraction sets to capture transitions that read a fresh letter from the input word. We prove a Kleene theorem for RNNAs w.r.t. a simple expression language that extends nominal Kleene algebra (NKA) with unscoped name binding, thus remedying the known failure of the expected Kleene theorem for NKA itself. We analyse RNNAs under two notions of freshness: global and local. Under global freshness, RNNAs turn out to be equivalent to session automata, and as such have a decidable inclusion problem. Under local freshness, RNNAs retain a decidable inclusion problem, and translate into register automata. We thus obtain decidability of inclusion for a reasonably expressive class of nondeterministic register automata, with no bound on the number of registers.



We thank Charles Paperman for useful discussions, and the anonymous reviewers of an earlier version of the paper for insightful comments that led us to discover the crucial notion of name dropping. Erwin R. Catesbeiana has commented on the empty bar language.


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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  • Lutz Schröder
    • 1
    Email author
  • Dexter Kozen
    • 2
  • Stefan Milius
    • 1
  • Thorsten Wißmann
    • 1
  1. 1.Friedrich-Alexander-Universität Erlangen-NürnbergErlangenGermany
  2. 2.Cornell UniversityIthacaUSA

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