The Conditional DAG (CDAG) task model is used for modeling multiprocessor real-time systems containing conditional expressions for which outcomes are not known prior to their evaluation. Feasibility analysis for CDAG tasks upon multiprocessor platforms is shown to be complete for the complexity class pspace; assuming np pspace, this result rules out the use of Integer Linear Programming solvers for solving this problem efficiently. It is further shown that there can be no pseudo-polynomial time algorithm that solves this problem unless p = pspace. CCS Concepts: • Computer systems organization → Embedded and cyber-physical systems; • Software and its engineering → Real-time schedulability; Scheduling;