We present a--yet unpublished-- generalization of the Algebraic Dynamic Programming framework which also accomodates problems on trees. The new framework is not an "add-on" extension, but suggests a reformulation of "classical" ADP. ADP 2.0 is not only more general, but (arguably) more elegant - and more difficult to implement. In fact, no general implementation technique is known at present. An ensemble of about 30 problems - most classical, some new - from biosequence and structure analysis has been described in the new framework.