  This paper studies the (discrete) \emph{chemical reaction network (CRN)}
computational model that emerged in the last two decades as an abstraction for
molecular programming. The correctness of CRN protocols is typically
established under one of two possible schedulers that determine how the
execution advances: (1) a \emph{stochastic scheduler} that obeys the
(continuous time) Markov process dictated by the standard model of stochastic
chemical kinetics; or (2) an \emph{adversarial scheduler} whose only commitment
is to maintain a certain fairness condition. The latter scheduler is justified
by the fact that the former one crucially assumes ``idealized conditions'' that
more often than not, do not hold in real wet-lab experiments. However, when it
comes to analyzing the \emph{runtime} of CRN protocols, the existing literature
focuses strictly on the stochastic scheduler, thus raising the research
question that drives this work: Is there a meaningful way to quantify the
runtime of CRNs without the idealized conditions assumption?
  The main conceptual contribution of the current paper is to answer this
question in the affirmative, formulating a new runtime measure for CRN
protocols that does not rely on idealized conditions. This runtime measure is
based on an adapted (weaker) fairness condition as well as a novel scheme that
enables partitioning the execution into short \emph{rounds} and charging the
runtime for each round individually (inspired by definitions for the runtime of
asynchronous distributed algorithms). Following that, we turn to investigate
various fundamental computational tasks and establish (often tight) bounds on
the runtime of the corresponding CRN protocols operating under the adversarial
scheduler. This includes an almost complete chart of the runtime complexity
landscape of predicate decidability tasks.
