This work examines the complexity of scheduling for high level synthesis. It has been shown that the problem of finding the minimum time schedule for a set of chains of operations of two types using two processors, one of each type, is NP-complete. However, for two chains only, a polynomial time algorithm can been obtained for scheduling with two processors. The problem of scheduling a rooted binary tree of two operation types on two processors, one of each type, has been shown to be NP-complete. It has also been proved that absolute approximations for schedule length minimization or processor minimization are NP-complete. A related resource constrained scheduling problem has also been shown to be NP-hard.

Keywords: Scheduling, NP-complete problems, High-Level Synthesis.