On the complexity of the generalized Q2R automaton
Eric Goles (Facultad de Ingenier\'ia y Ciencias, Universidad Adolfo, Ib\'a\~nez, Santiago, Chile), Marco Montalva-Medel (Facultad de Ingenier\'ia, y Ciencias, Universidad Adolfo Ib\'a\~nez, Santiago, Chile), Pedro, Montealegre (Facultad de Ingenier\'ia y Ciencias
TL;DR
This paper investigates the complexity of the generalized Q2R automaton, revealing non-polynomial cycles, its simulation capabilities, and proving that node state change decision is P-Hard.
Contribution
It introduces the complexity analysis of the generalized Q2R automaton, including cycle existence, simulation equivalence, and computational hardness results.
Findings
Existence of non-polynomial cycles in the automaton
Automaton can simulate classical Q2R with block sequential updates
Deciding if a node changes state is P-Hard
Abstract
We study the dynamic and complexity of the generalized Q2R automaton. We show the existence of non-polynomial cycles as well as its capability to simulate with the synchronous update the classical version of the automaton updated under a block sequential update scheme. Furthermore, we show that the decision problem consisting in determine if a given node in the network changes its state is \textbf{P}-Hard.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
Topicssemigroups and automata theory · Formal Methods in Verification · DNA and Biological Computing