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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

Acknowledgements

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

Cite As Get BibTex

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) https://doi.org/10.4230/LIPIcs.CONCUR.2023.33

Abstract

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
Keywords
  • memory automata
  • ν-automata
  • LaMA
  • HRA
  • complexity
  • non-emptiness
  • membership

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