This paper defines conditions for a Signal Transition Graph to be implemented by an asynchronous circuit. A hierarchy of the implementability classes is presented. Our main concern is the implementability of the specification under the restricted input-output interface between the design and the environment, i.e., when no additional interface signals are allowed to be added to the design. We develop algorithms and present experimental results of using BDD-traversal for checking STG implementability. These results demonstrate efficiency of the symbolic approach and show a way of improving existing tools for STG-based asynchronous circuit design.