Synthetic biology is founded on the central dogma of molecular biology, which describes flow of genetic information from DNA to RNA to Protein. Using this foundation as a platform for logic synthesis, biologists have engineered genetic modules that can resemble logical functions such as a NOR gate (logical joint denial). Although a NOR gate is a universal gate (it can be used to implement any combinatorional logic circuit without the need to use any other gate type), Boolean functions lack the functional richness required to capture the finer details of molecular biology. Furthermore, sparse or poorly defined characterization of genetic modules makes creating robust genetic circuits difficult. To solve these problems, this work uses the principles of systems engineering, and introduces a framework to build reliable and robust genetic systems.
We developed a sampling-based motion planning algorithm that combines long-term temporal logic goals with short-term reactive requirements. The mission specification has two parts: (1) a global specification given as a Linear Temporal Logic (LTL) formula over a set of static service requests that occur at the regions of a known environment, and (2) a local specification that requires servicing a set of dynamic requests that can be sensed locally during the execution. The proposed computational framework consists of two main ingredients: (a) an off-line sampling-based algorithm for the construction of a global transition system that contains a path satisfying the LTL formula, and (b) an on-line sampling-based algorithm to generate paths that service the local requests, while making sure that the satisfaction of the global specification is not affected. The off-line algorithm has three main features. First, it is incremental, in the sense that the procedure for finding a satisfying path at each iteration scales only with the number of new samples generated at that iteration. Second, the underlying graph is sparse, which guarantees the low complexity of the overall method. Third, it is probabilistically complete. We also provide a conditional result showing that the incremental checking procedure has the best possible complexity bound. The on-line algorithm leverages ideas of potential functions, which ensure progress towards satisfaction of the global specification, and on monitors for LTL. Examples illustrating the usefulness and the performance of the framework are included.