This project aims to significantly advance the field of synthetic biology by introducing new paradigms and techniques for programming biological systems and for understanding the computations performed by living cells. Synthetic biology is truly a great revolution in the offing but has failed to scale well on programmable complexity. One reason for this failure has been the overemphasis on digital paradigms. In this project, we demonstrate how to get rid of this limitation by advancing the state-of-the-art in the DNA strand displacement (DSD) theory to synthesize programmable hybrid dynamical circuits using DNA, RNA, and enzymes. Our approach lays the foundation for a unifying framework for the design of computational nucleic acid devices and helps answer previously unexplored important questions such as "How long will a given biomolecular circuit perform reliably in the wet-lab settings?" and "How robust is a given biomolecular circuit to the interference created by the extraneous cellular reactions in the wet-lab settings?" The computational nucleic acid devices synthesized using our approach show great potential for enabling a broad range of biotechnology applications, including smart probes for molecular biology research, in vitro assembly of complex compounds, high-precision in vitro disease diagnosis and, ultimately, programmable sense-and-respond systems inside living cells. This diversity of applications is supported by a range of implementation strategies, including nucleic acid strand displacement, localization to substrates, and the use of enzymes with polymerase, nickase, and exonuclease functionality. However, existing computational design tools are unable to account for these strategies in a unified manner. Hence, we also code our theoretical approach a logic programming language that allows a broad range of computational nucleic acid systems to be designed and analyzed. The language extends standard logic programming with a novel equational theory to express nucleic acid molecular motifs. It automatically identifies matching motifs present in the full system, in order to apply a specified transformation expressed as a logical rule or as a dynamical system output. The language is sufficiently expressive to encode the semantics of nucleic strand displacement systems with complex topologies, together with computation performed by a broad range of enzymes, and is readily extensible to new implementation strategies. The language development is in collaboration with Microsoft Research (Cambridge, UK) and has resulted in the software "Visual DSD" that facilitates a user-friendly in silico design of such biomolecular circuits - the software "Visual DSD" runs on both Windows and MacOS platforms, and can be coupled to other computational platforms such as MATLAB and Python. One of the core problems in the synthesis of such biomolecular circuits is the choice of kinetic rates. Recently, Nielsen et al at the Massachusetts Institute of Technology (Cambridge, MA) have developed the platform "Cello" for an automated designed of such circuits. All the same, the design procedure of Cello is limited to only Boolean circuits and does not make use of artificial intelligence and public domain metadata to increase the accuracy and the range of operating conditions over which the circuits function as desired. We demonstrate how the novel biochemical insights developed in this project can help synthesize non-Boolean circuits (such as a low-pass filter or ratio computation or logarithm) and hybrid systems using DNA/RNA/enzymes and to dramatically increase the yield of cell-free protein synthesis (CFPS) systems in the wet-lab. Such a translational impact of the project will be achieved through collaborations with Microsoft Research (Cambridge, UK) and Arbor Bioscience (Ann Arbor, MI).