On the complexity of occurrence and convergence problems in reaction systems

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

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

Reaction systems are a model of computation inspired by biochemical reactions introduced by Ehrenfeucht and Rozenberg. Two problems related to the dynamics (the evolution of the state with respect to time) of reaction systems, namely, the occurrence and the convergence problems, were recently investigated by Salomaa. In this paper, we prove that both problems are PSPACE-complete when the numerical parameter of the problems (i.e. the time step when a specified element must appear) is given as input. Moreover, they remain PSPACE-complete even for minimal reaction systems.

Mots clés: Reaction systems; Computational complexity; Discrete dynamical systems

Domaines: Informatique [cs]; Complexité [cs.CC]; Mathématique discrète [cs.DM]; Systèmes dynamiques [math.DS]

Enrico Formenti, Luca Manzoni, Antonio Enrico Porreca. On the complexity of occurrence and convergence problems in reaction systems. Natural Computing, 2015, 14 (1), pp.185-191. ⟨hal-01313680⟩