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Complexity of Membership and Non-Emptiness Problems in Unbounded Memory Automata

Authors Clément Bertrand , Cinzia Di Giusto , Hanna Klaudel , Damien Regnault

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Author Details

Clément Bertrand
  • Scalian Digital Systems, Valbonne, France
Cinzia Di Giusto
  • Université Côte d’Azur, CNRS, I3S, France
Hanna Klaudel
  • IBISC, Univ. Evry, Université Paris-Saclay, France
Damien Regnault
  • IBISC, Univ. Evry, Université Paris-Saclay, France


We want to thank the anonymous reviewers for the careful reviews and insightful comments.

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Clément Bertrand, Cinzia Di Giusto, Hanna Klaudel, and Damien Regnault. Complexity of Membership and Non-Emptiness Problems in Unbounded Memory Automata. In 34th International Conference on Concurrency Theory (CONCUR 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 279, pp. 33:1-33:17, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)


We study the complexity relationship between three models of unbounded memory automata: nu-automata (ν-A), Layered Memory Automata (LaMA)and History-Register Automata (HRA). These are all extensions of finite state automata with unbounded memory over infinite alphabets. We prove that the membership problem is NP-complete for all of them, while they fall into different classes for what concerns non-emptiness. The problem of non-emptiness is known to be Ackermann-complete for HRA, we prove that it is PSPACE-complete for ν-A.

Subject Classification

ACM Subject Classification
  • Theory of computation → Automata over infinite objects
  • Theory of computation → Problems, reductions and completeness
  • memory automata
  • ν-automata
  • LaMA
  • HRA
  • complexity
  • non-emptiness
  • membership


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