Detecting State Encoding Conflicts in STG Unfoldings Using SAT

The behaviour of asynchronous circuits is often described by Signal Transition Graphs (STGs), which are Petri nets whose transitions are interpreted as rising and falling edges of signals. One of the crucial problems in the synthesis of such circuits is that of identifying whether an STG satisfies the Complete State Coding (CSC) requirement (which states that semantically different reachable states must have different binary encodings), and, if necessary, modifying the STG (by, e.g. inserting new signals helping to trace the current state) to meet this requirement. This is usually done using reachability graphs. In this paper, we avoid constructing the reachability graph of an STG, which can lead to state space explosion, and instead use only the information about causality and structural conflicts between the events involved in a finite and complete prefix of its unfolding. We propose an efficient algorithm for detection of CSC conflicts based on the Boolean Satisfiability (SAT) approach. Following the basic formulation of the state encoding conflict relationship, we present some problem-specific optimization rules. Experimental results show that this technique leads not only to huge memory savings when compared to the CSC conflicts detection methods based on reachability graphs, but also to significant speedups in many cases.