On the Complexity of Consistency and Complete State Coding for Signal Transition Graphs

Signal Transition Graphs (STGs) are a popular formalism for the specification of asynchronous circuits. A necessary condition for the implementability of an STG is the existence of a consistent and complete state encoding. For an important subclass of STGs, the marked graph STGs, we show that checking consistency is polynomial, but checking the existence of a complete state coding is co-NP-complete. In fact, co-NP-completeness already holds for acyclic and 1-bounded marked graph STGs and for live and 1-bounded marked graph STGs. We add some relevant results for freechoice, bounded, and general STGs.