Figure 3.

Implementing all Boolean logic functions using a reduced number of computational devices. (A) Schematics of all devices needed to implement up to 4-input functions. (B) Maximum number of strains and number of computational devices needed to compute all Boolean functions for a given number of inputs. See Methods for details. (C) Proportion of Boolean functions implementable with a specific number of strains for 3 and 4 inputs (obtained by generating all the biological designs for 3 and 4-input Boolean functions, see Table S1 for numbers). (D) Example of a biological implementation for a 4-input Boolean function. The function shown here is divided into a disjunction of conjunctive clauses (see Figure 2A). Each conjunctive clause is executed using a particular computational device (defined in panel A) each placed into a separate cellular computing unit. By combining the different units, the full logic function is obtained. If at least one of the cellular units is ON, the output is considered to be ON. Of note, inputs are not always connected to the same integrase (as for input D in Cell 1 and Cell 2), and all integrases and inputs are not present in all cells.