Bisimulation under constrained configuration maps

Determine whether restricting the configuration map in the paper's polynomial efficient simulation framework to be consistent with an underlying species-to-species mapping yields weak bisimulation between the simulated and simulating chemical reaction network systems, and ascertain whether additionally requiring that underlying map to be a total bijection yields strong bisimulation.

Background

The paper introduces a general-purpose notion of polynomial efficient simulation for chemical reaction network (CRN) variants, using configuration maps and macrotransitions to relate systems while accounting for efficiency in species, rules, time, and volume. This framework is more permissive than classical bisimulation and is intended to capture a broader notion of simulation that remains practical for complexity analyses.

The authors pose whether certain restrictions on the configuration map could recover established notions from process theory: specifically, whether consistency with a species-to-species mapping corresponds to weak bisimulation, and if a total bijective mapping corresponds to strong bisimulation. Resolving this would clarify how their simulation framework relates to standard equivalence notions.