# Complexity of the dynamics of reaction systems

## TL;DR

This paper explores the computational complexity of various dynamical behaviors in reaction systems, revealing a spectrum from tractable to PSPACE-complete problems, thereby advancing understanding of their computational properties.

## Contribution

It provides a comprehensive analysis of the decision problems related to reaction systems' dynamics and classifies their computational complexity.

## Key findings

- Decision problems range from tractable to PSPACE-complete.
- Complexity classifications include fixed points, cycles, attractors, and reachability.
- The work enhances understanding of the computational limits of reaction systems.

## Abstract

Reaction systems are discrete dynamical systems inspired by bio-chemical processes, whose dynamical behaviour is expressed by set-theoretic operations on finite sets. Reaction systems thus provide a description of bio-chemical phenomena that complements the more traditional approaches, for instance those based on differential equations. A comprehensive list of decision problems about the dynamical behavior of reaction systems (such as cycles and fixed/periodic points, attractors, and reachability) is provided along with the corresponding computational complexity, which ranges from tractable problems to PSPACE-complete problems.