Fig 1.
(a) An example of a Boolean network. (b) the state transition table of this Boolean network.
Fig 2.
Example of a Boolean network control problem.
(a) Network, (b) its state transition rules, (c) Control problem and its solution.
Fig 3.
Pseudo-code of our proposed algorithm.
Fig 4.
Example of a network with four non-branching single node components.
Fig 5.
An example of a branching node that is not able to attain both states 0 and 1 in a time step.
Fig 6.
Example of a network, its transition function, and its initial and desired states.
Table 1.
State space for the SCC S1 for the network represented in Fig 6.
Table 2.
Value of ϒ table for SCC S2 for the network represented in Fig 6.
Table 3.
Value of ϒ table after processing SCCs S1, S2, and S3 and before processing SCC S4 for the network represented in Fig 6.
Fig 7.
A schematic view of the topology of single node non-branching components between other SCCs of a network.
Cloudy nodes are either branching single node or multi-node components (hard components). Normal circles represent single node non-branching components (simple components). Simple components make a rooted tree toward their roots.
Fig 8.
Example of applying the transformation of removing simple components from a network to obtain a simple component-free extended network.
Fig 9.
Boolean network model of Drosophila melanogaster.
Dotted lines indicate a multi-node component, and the numberings beside nodes indicate topological orders. Nodes indicated as rectangles, i.e. nodes U1, U2, and U3, are external nodes.
Table 4.
Evolution functions for the Boolean network model of Drosophila melanogaster.
Fig 10.
Boolean network model of T-cell receptor.
Network’s graph has one multi-node component. The numberings beside each node indicate their topological ordering.
Table 5.
Initial state and desirable state of each node for Drosophila melanogaster network’s graph.
Table 6.
Initial states and desirable states of each node in T-cell receptor kinetics network graph.
Table 7.
Comparison of algorithms for a control problem on the T-cell network’s receptor kinetics (Table 6) and Drosophila melanogaster’s network (Table 5).