A synthetic approach to biology is a promising technique for various applications. Recent advancements have demonstrated the feasibility of constructing synthetic two-input logic gates in Escherichia coli cells with long-term memory based on DNA inversion induced by recombinases. Moreover, recent evidences indicate that DNA inversion mediated by genome editing tools is possible. Powerful genome editing technologies, such as CRISPR-Cas9 systems, have great potential to be exploited to implement largescale recombinase-based circuits. What remains unclear is how to construct arbitrary Boolean functions based on these emerging technologies. In this paper, we lay the theoretical foundation formalizing the connection between recombinase-based genetic circuits and Boolean functions. It enables systematic construction of any given Boolean function using recombinase-based logic gates. We further develop a methodology leveraging existing electronic design automation (EDA) tools to automate the synthesis of complex recombinase-based genetic circuits with respect to area and delay optimization. In silico experimental results demonstrate the applicability of our proposed methods as a useful tool for recombinase-based genetic circuit synthesis and optimization.The development of synthetic biology shows the feasibility to implement computing devices with DNA genetic circuits in living cells. Synthetic cellular designs often intended to implement certain functions that make cells respond to specific environmental stimuli or even change their growth and cellular development. For instance, synthetic toggle switches 1 and genetic oscillators 2-5 can be used to control cell metabolism, synthetic counters 6 can be potentially applied to the regulation of telomere length and cell aggregation, and genetic logic gates [7][8][9][10] can achieve digital computation in response to stimulus input signals. In addition to these transcription-based DNA circuits, new emerging translational mRNA circuits 11 are likely to have impact on mammalian regenerative medicine and gene therapy. Through the genetic engineering, synthetic cellular circuits are potentially useful to perform therapeutic and diagnostic functions.For some situations where noxious chemical stimuli exist for many cell generations, the computational results from the synthetic circuits in parent cells are required to be propagated to their daughter cells so that the daughter cells can save time to respond to the environmental stimuli. To achieve this transgenerational memory, one possible method is to store the computational results in separate synthetic memory devices which can be duplicated in cell divisions. In the recent work of Siuti et al.12 , a more efficient scheme for constructing synthetic cellular circuits with integrated logic and memory was proposed, where the computational result was automatically stored in the computing circuit configuration and the changes of configuration can be propagated to its descendant cells. The so-implemented circuits were built based on re...