Dynamic Controllability of Conditional Simple Temporal Networks is   PSPACE-complete
  Even after the proposal of various solution algorithms, the precise computational complexity of checking whether a Conditional Temporal Network is Dynamically Controllable had still remained widely open. This issue gets settled in this paper which provides constructions, algorithms, and bridging lemmas and arguments to formally prove that: (1) the problem is PSPACE-hard, and (2) the problem lies in PSPACE. 
Massimo Cairo and Romeo Rizzi
cs.DS