Reply to "Input-output decomposition of dynamic systems is NP-complete"

The authors consider R.E. Tarjan's note (see ibid., pp. 863-864) an interesting observation regarding the input-output decomposition scheme for dynamic systems. It is an appropriate warning in the attempts to consider very large-scale dynamic systems using the scheme, where not only the number of states, but also the number of acyclic components becomes prohibitive. At present, however, this is not an important consideration because the dynamic part of problems in large systems would saturate numerically way before the graph decomposition algorithms would. This is especially true because the number of states in a dynamic system is typically much larger than the number inputs and outputs, thus making the NP-completeness a less significant aspect of the problem. Furthermore, the input-output decomposition scheme may be helpful even in systems of modest size, where NP-completeness is not a factor because of a decrease in online computations offered by the hierarchical design schemes.