eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-03-10
32:1
32:17
10.4230/LIPIcs.STACS.2021.32
article
Rice-Like Theorems for Automata Networks
Gamard, Guilhem
1
Guillon, Pierre
2
Perrot, Kevin
1
3
Theyssier, Guillaume
2
Aix-Marseille Université, Université de Toulon, CNRS, LIS, Marseille, France
Aix-Marseille Université, CNRS, I2M, Marseille, France
Université Côte d'Azur, CNRS, I3S, Sophia Antipolis, France
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol187-stacs2021/LIPIcs.STACS.2021.32/LIPIcs.STACS.2021.32.pdf
Automata networks
Rice theorem
complexity classes
polynomial hierarchy
hardness