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We analyze the solutions, on single network instances, of a recentlyintroduced class of constraint-satisfaction problems (CSPs), describingfeasible steady states of chemical reaction networks. First, we show that theCSPs generalize the scheme known as Network Expansion, which is recovered in aspecific limit. Next, a full statistical mechanics characterization (includingthe phase diagram and a discussion of physical origin of the phase transitions)for Network Expansion is obtained. Finally, we provide a message-passingalgorithm to solve the original CSPs in the most general form.

Searching for feasible stationary states in reaction networks by solving a Boolean constraint satisfaction problem