Chapter

Descriptional Complexity of Formal Systems

Volume 8614 of the series Lecture Notes in Computer Science pp 114-125

Cycles and Global Attractors of Reaction Systems

  • Enrico FormentiAffiliated withUniv. Nice Sophia Antipolis, CNRS, I3S, UMR 7271
  • , Luca ManzoniAffiliated withUniv. Nice Sophia Antipolis, CNRS, I3S, UMR 7271
  • , Antonio E. PorrecaAffiliated withDipartimento di Informatica, Sistemistica e Comunicazione, Università degli Studi di Milano-Bicocca

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Abstract

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.