Algorithms for Enumerating Irreducible and Closed Autocatalytic Sets

Autocatalytic sets are chemical reaction networks in which the molecules mutually catalyze each other's formation supported by an ambient food set. They are believed to have played an important role in the origin of metabolism and life, and have been studied extensively both theoretically and experimentally. Autocatalytic sets often consist of a hierarchical structure of smaller and smaller autocatalytic subsets. Of particular interest are irreducible autocatalytic sets and closed autocatalytic sets. Previously, it has been shown that finding {\it all} such autocatalytic subsets is, in principle, intractable. Here, several algorithms are presented to enumerate irreducible and closed autocatalytic sets, either exhaustively (but only practical in limited cases) or in the form of a random sample. Their implementation in a C++ program, made available as a GitHub repository, is then tested on instances of a computational model of chemical reaction networks known as the binary polymer model.