It is easy to remark that CPDL has more expressive power than PDL. To see this, consider the CPDL formula &lt;π-1&gt;1 and the LTSs M = (W, R, V) and M′ = (W′, R′, V′) where W = {x,y}, R(π) = {(x,y)}, W′ = {y′}, R′(π) = ∅  and V(x) = V(y)  = V′(y′) =  ∅. Since M, y sat &lt;π-1&gt;1,  not M′, y′ sat  &lt;π-1&gt;1, and because for all PDL  formulas A it is the case that M, y sat A iff M′, y′ sat A, then it is clear that no PDL formula is equivalent to &lt;π-1&gt;1.