Ancestors, descendants, and gardens of Eden in reaction systems

Creators: Dennunzio, Alberto; Formenti, Enrico; Manzoni, Luca; Porreca, Antonio

Others:: Dipartimento di Informatica Sistemistica e Comunicazione (DISCo) ; Università degli Studi di Milano-Bicocca = University of Milano-Bicocca (UNIMIB); Modèles Discrets pour les Systèmes Complexes (Laboratoire I3S - MDSC) ; Laboratoire d'Informatique, Signaux, et Systèmes de Sophia Antipolis (I3S) ; Université Nice Sophia Antipolis (1965 - 2019) (UNS) ; COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS) ; COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA); Laboratoire d'Informatique, Signaux, et Systèmes de Sophia Antipolis (I3S) ; Université Nice Sophia Antipolis (1965 - 2019) (UNS) ; COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)

Description

This paper analyses several problems related to finding and counting ancestor and descendant states, as well as gardens of Eden (i.e., states without predecessors) in reaction systems. The focus is on the complexity of finding and counting preimages and ancestors that are minimal with respect to cardinality. It turns out that the problems concerning gardens of Eden seem to require the presence of an NP-oracle to be solved. All the problems studied are intractable, with a complexity that ranges form FPNP[log⁡n] to FPSPACE(poly).

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Ancestors, descendants, and gardens of Eden in reaction systems

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