Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH scholarly article en Gamard, Guilhem; Guillon, Pierre; Perrot, Kevin; Theyssier, Guillaume https://www.dagstuhl.de/lipics License: Creative Commons Attribution 4.0 license (CC BY 4.0)
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URN: urn:nbn:de:0030-drops-136770
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Rice-Like Theorems for Automata Networks

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Abstract

We prove general complexity lower bounds on automata networks, in the style of Rice’s theorem, but in the computable world. Our main result is that testing any fixed first-order property on the dynamics of an automata network is either trivial, or NP-hard, or coNP-hard. Moreover, there exist such properties that are arbitrarily high in the polynomial-time hierarchy. We also prove that testing a first-order property given as input on an automata network (also part of the input) is PSPACE-hard. Besides, we show that, under a natural effectiveness condition, any nontrivial property of the limit set of a nondeterministic network is PSPACE-hard. We also show that it is PSPACE-hard to separate deterministic networks with a very high and a very low number of limit configurations; however, the problem of deciding whether the number of limit configurations is maximal up to a polynomial quantity belongs to the polynomial-time hierarchy.

BibTeX - Entry

@InProceedings{gamard_et_al:LIPIcs.STACS.2021.32,
  author =	{Gamard, Guilhem and Guillon, Pierre and Perrot, Kevin and Theyssier, Guillaume},
  title =	{{Rice-Like Theorems for Automata Networks}},
  booktitle =	{38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021)},
  pages =	{32:1--32:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-180-1},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{187},
  editor =	{Bl\"{a}ser, Markus and Monmege, Benjamin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/13677},
  URN =		{urn:nbn:de:0030-drops-136770},
  doi =		{10.4230/LIPIcs.STACS.2021.32},
  annote =	{Keywords: Automata networks, Rice theorem, complexity classes, polynomial hierarchy, hardness}
}

Keywords: Automata networks, Rice theorem, complexity classes, polynomial hierarchy, hardness
Seminar: 38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021)
Issue date: 2021
Date of publication: 10.03.2021


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