Algorithm 1 State Space Exploration

INPUT:nk, MAX, Initial State

OUTPUT:TransitionMatrixn, StateListn

1: initialize: NextTierQueue←Initial State, Queue←∅

2: initialize: StateList←Initial State, TransitionMatrix←∅

3: for Tier ∊ (2, MAX) do

4:  Queue←NextTierQueue

5:  NextTierQueue←∅

6:  for all states s∊Queuedo

7:   for all non-empty voxels v∊sdo

8:    for all inter-voxel transitions d {with probabilities p(d)} originating from vdo

9:     find state t←s+d(v)

10:     ift∉StateListthen

11:      add t to StateList, add t to NextTierQueue

12:     end if

13:     TransitionMatrix(s,t)←p(d)

14:    end for

15:   end for

16:  end for

17: end for

18: Update Diagonal elements in TransitionMatrix

19: Truncate TransitionMatrix so that it is of dimension |StateList|

20: Create absorbing state in TransitionMatrix