Solvability of simultaneous control step and timing skew assignments in high level synthesis

The simultaneous optimization of the control step assignment and the control skew assignment is a powerful technique in improving performance. This paper treats an essential and important problem, the solvability of this simultaneous control step and timing skew assignments. Our first result is to announce that the decision problem whether an input instance has a feasible pair of control step assignment and timing skew assignment or not is NP-complete. The second result is to show the necessary and sufficient condition for an input instance to have feasible solutions for every clock period. The latter result contributes greatly to designing a heuristic algorithm for the simultaneous optimization of control step and timing skew assignments, which has been proven to be NP-hard.