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Algebraic properties of automata associated to Petri nets and applications to computation in biological systems

<10> This article shows how to apply computational Krohn-Rhodes algebraic automata methods to Petri nets, commonly used to describe biological systems such as gene regulatory networks. It proves that, for a large class of Petri nets, inhibition is necessary for non-trivial reversible subsystems to arise, and shows constructively that every finite semigroup embeds into the semigroup of a Petri net. Automatic computational analysis demonstrates comparable results to other automata-theoretic models of biological networks. This extends our computational algebraic methods, now exploited world-wide including in the FP7 FET BIOMICS project, to Petri net models in systems biology and other fields.