Cycles and Global Attractors of Reaction Systems

Enrico Formenti (1, 2) , Luca Manzoni (1, 2) , Antonio Enrico Porreca (3)

1 I3S - Laboratoire d'Informatique, Signaux, et Systèmes de Sophia Antipolis
2 Laboratoire I3S - MDSC - Modèles Discrets pour les Systèmes Complexes
3 DISCo - Dipartimento di Informatica Sistemistica e Comunicazione

Reaction systems are a recent formal model inspired by the chemical reactions that happen inside cells and possess many different dynamical behaviours. In this work we continue a recent investigation of the complexity of detecting some interesting dynamical behaviours in reaction system. We prove that detecting global behaviours such as the presence of global attractors is PSPACE - complete. Deciding the presence of cycles in the dynamics and many other related problems are also PSPACE - complete. Deciding bijectivity is, on the other hand, a coNP - complete problem.

Mots clés: reaction systems; computational complexity

Domaines: Informatique [cs]; Complexité [cs.CC]; Mathématique discrète [cs.DM]; Systèmes dynamiques [math.DS]; Automates cellulaires et gaz sur réseau [nlin.CG]; Dynamique Chaotique [nlin.CD]; Adaptation et Systèmes auto-organisés [nlin.AO]

Enrico Formenti, Luca Manzoni, Antonio Enrico Porreca. Cycles and Global Attractors of Reaction Systems. Descriptional Complexity of Formal Systems (DFCS 2014), Helmut Jürgensen; Juhani Karhumäki; Alexander Okhotin, Aug 2014, Turku, Finland. pp.114-125, ⟨10.1007/978-3-319-09704-6_11⟩. ⟨hal-01312662⟩