Boolean controllers for systems with complex datapaths are often very difficult to implement correctly, in particular when concurrency is involved. Yet, in many instances it is easy to formally specify correctness. For example, the specification for the controller of a pipelined processor only has to state that the pipelined processor gives the same results as a non-pipelined reference design. This makes such controllers a good target for automated synthesis. However, an efficient abstraction for the complex datapath elements is needed, as a bit-precise description is often infeasible. We present Suraq, the first controller synthesis tool which uses uninterpreted functions for the abstraction. Quantified first-order formulas (with specific quantifier structure) serve as the specification language from which Suraq synthesizes Boolean controllers. Suraq transforms the specification into an unsatisfiable SMT formula, and uses Craig interpolation to compute its results. Using Suraq, we were able to synthesize a controller (consisting of two Boolean signals) for a five-stage pipelined DLX processor in roughly one hour and 15 minutes.
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