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DOI: 10.4230/LIPIcs.CONCUR.2023.33
Complexity of Membership and Non-Emptiness Problems in Unbounded Memory Automata

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

Published in: LIPIcs, Volume 279, 34th International Conference on Concurrency Theory (CONCUR 2023)

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.
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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)

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@InProceedings{bertrand_et_al:LIPIcs.CONCUR.2023.33,
  author =	{Bertrand, Cl\'{e}ment and Di Giusto, Cinzia and Klaudel, Hanna and Regnault, Damien},
  title =	{{Complexity of Membership and Non-Emptiness Problems in Unbounded Memory Automata}},
  booktitle =	{34th International Conference on Concurrency Theory (CONCUR 2023)},
  pages =	{33:1--33:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-299-0},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{279},
  editor =	{P\'{e}rez, Guillermo A. and Raskin, Jean-Fran\c{c}ois},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2023.33},
  URN =		{urn:nbn:de:0030-drops-190277},
  doi =		{10.4230/LIPIcs.CONCUR.2023.33},
  annote =	{Keywords: memory automata, \nu-automata, LaMA, HRA, complexity, non-emptiness, membership}
}
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