Gamard, Guilhem
[Verfasser:in];
Guillon, Pierre
[Verfasser:in];
Perrot, Kevin
[Verfasser:in];
Theyssier, Guillaume
[Verfasser:in]
;
Guilhem Gamard and Pierre Guillon and Kevin Perrot and Guillaume Theyssier
[Mitwirkende:r]
Anmerkungen:
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Beschreibung:
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.