Fig. 2

Converging tree of the example network. a The desired phenotype value P = 0 in the 0th level. b The signals for {P = 0} in the 0th level are {C = 0} and {E = 0}. The left box denotes the two solutions {C = 0} and {E = 0} of the eq. 0 = C&E coming from the update rule P* = C&E for P. The two solutions are the children sets of the 0th-level parent set {P = 0} in the right tree. c The signals for {C = 0} and signals for {E = 0} in the 1st level. The signals for {C = 0} are obtained from the update rule C* = (!B)&D&E and they are {B = 1}, {D = 0} and {E = 0}, solutions of the eq. 0 = (!B)&D&E. Similarly the signal for {E = 0} is the unique solution {(D, F) = (0,0)} of the eq. 0 = D|F obtained from the update rule E* = D|F. The four solutions are children sets in the 2nd level. Each control set with a dotted circle denotes a removed control set that is found by using the two removal rules. The term ‘leaf {E = 0}’ means that {E = 0} is a leaf set. The meanings of terms and symbols in (d) are the same as those in (c). e The final converging tree with six control sets up to the last level (see Additional file 1 for details)