Movie S1.

Animation explaining the computation principle. In this animation, a network encoding the {1,3} SSP is explained and an example agent is shown to travel the path that encodes the subset {3}. The agent enters the network from the top left-hand corner. It first encounters a split junction where it randomly decides to turn right and exclude the corresponding number. The agent then enters another split junction, where it adds the corresponding number to the subset. The number of pass junctions following each split junction determines the actual value of the integer added to the subset at the respective split junction. The exit numbers correspond to the target sums T (potential solutions) represented by each exit. The example agent arrives at the exit #3 corresponding to the total sum of the subset {3} the agent explored. Finally, the correct results (labeled in green) and incorrect results (where no agents will arrive; labeled in magenta) for this particular set {1, 3} are explained.