Algebraic GPAC to CRN Compiler

GPAC dynamics are continuous — differential equations over real-valued signals. CRN reactions are discrete — integer-valued molecular counts governed by mass-action kinetics. Bridging those two without losing the mathematical meaning of the original specification is the core difficulty of the entire problem.

Fix. A formal framework using category theory to establish semantic equivalence, with bisimulation checking as the runtime verification method. Every generated CRN is tested for behavioral correspondence against the input GPAC before it leaves the compiler.

Naively translated CRNs grow exponentially. A moderately complex GPAC specification produces a CRN with so many species and reactions that no molecular implementation could handle it.

Fix. Algebraic simplification passes that identify equivalent species and merge them during compilation, reducing the reaction set to a minimum. Constraint satisfaction search finds the smallest set of reactions that produces the correct computational behavior.

CRN reactions don't execute instantly — their speed is governed by rate constants that determine how quickly species concentrations change. The correct constants aren't obvious from the GPAC equations, and wrong constants produce a CRN that computes the wrong answer at the right topology.

Fix. A rate constant inference algorithm grounded in mass-action kinetics, followed by numerical simulation to validate that generated CRNs converge to the correct output values before the compilation is considered complete.