Synthetic biology is applying engineering concepts to biological processes to enable genetic circuit designs, among other applications. As more biological parts are being discovered, it is vital to have an automated procedure to allow complex circuit designs to be built. Technology mapping is a set of procedures that maps biological components to a design specification. Current technology mapping frameworks for genetic circuits are used to design combinational circuits. This dissertation illustrates the process of building an automated workflow for a technology mapping framework to design synchronous sequential genetic circuits. An automated process to create a library of gates for logic and memory circuits is described to construct gates from DNA parts retrieved from a standardize data repository. Genetic constraints address what parts can be mapped to the design specification when the gates and designs are constructed. The proposed automaton workflow begins with a specification provided in a formal design language, such as Verilog. The input design specification is converted into a genetic regulatory network represented using the Synthetic Biology Open Language (SBOL). The network is decomposed into base functions (NOR gates, inverters, and genetic toggle switches) and matching and covering algorithms are performed to produce the output design. The output design is converted to the Systems Biology Markup Language (SBML) data format for testing and simulation. The outcome of this work provides the synthetic biology community insights on how asynchronous sequential circuit designs can be built through an automated procedure to perform technology mapping from libraries composed of logic gates and memory circuits.