In an embedded system including a base processor integrated with a tightly coupled accelerator, extracting frequently executed portions of the code (hot portion) and executing their corresponding data flow graph (DFG) on the accelerator brings about more speedup. In this paper, we intend to present our motivations for handling control instructions in DFGs and extending them to Control DFGs (CDFGs). In addition, basic requirements for an accelerator with conditional execution support are proposed. Moreover, some algorithms are presented for temporal partitioning of CDFGs considering the target accelerator architectural specifications. To show the effectiveness of the proposed ideas, we applied them to the accelerator of an extensible processor called AMBER. Experimental results represent the effectiveness of covering control instructions and using CDFGs versus DFGs.