Generating and checking control logic in the HDL-based design of reversible circuits

Although different from the conventional computing paradigm, reversible computation received significant interest due to its applications in various (emerging) technologies. Here, computations can be executed not only from the inputs to the outputs, but also in the reverse direction. This leads to significantly different design challenges to be addressed. In this work, we consider problems that occur when describing a reversible control flow using Hardware Description Languages (HDLs). Here, the commonly used conditional statements must, in addition to the established if-condition for forward computation, be provided with an additional fi-condition for backward computation. Unfortunately, deriving correct and consistent fi-conditions is often not obvious. Moreover, HDL descriptions exist which may not be realized with a reversible control flow at all. In this work, we propose automatic solutions which generate the required fi-conditions and check whether a reversible control flow indeed can be realized. The solution utilizes predicate transformer semantics based on Hoare logic. This has exemplary been implemented for the reversible HDL SyReC and evaluated with a variety of circuit description examples. The proposed solution constitutes the first automatic method for these important designs steps in the domain of reversible circuit design.