systems usually require abundant inputs to guarantee equivalent output signals that can be detected or distinguished, the strategies that are able to convert weak inputs to strong outputs are highly desired for high order logic operations and highly sensitive sensing. In recent years, researchers have made, and continue to make efforts to develop advanced synthetic DNA circuit systems for biological engineering. Dynamic DNA assembly which is concerned primarily with the construction of DNA circuits or nanostructures based on DNA hybridization attracted increasing research interests. [7][8][9] Especially, the dynamic and isothermal cyclic reactions such as hybridization chain reaction (HCR) and catalytic hairpin assembly (CHA) have been extensively utilized as robust strategies of enzymefree signal amplification in molecular recognition and sensing. [10,11] HCR is an established technique to obtain duplex DNA nanowires via the initiator-triggered cross-opening of hairpin reactants, which usually contributed to significant signal amplification and ease of operation in bio/chemosensing. [12][13][14] CHA is realized through initiator-catalyzed hybridizations of different DNA hairpins and thus result in the accumulation of short duplex DNA products. [15,16] Despite the advantages and achievements in signal amplification, these unitary DNA assembly strategies usually suffer from the signal leakage and limited amplification depth, which greatly hindered their applications in precisely sensing and profiling biomarkers with trace amounts.The advanced HCR and CHA, as well as the cascade integration of them are anticipated to theoretically offer improved amplification depth and stronger anti-interference capacity to break through the primary obstacles of their widely applications in sensing. For instance, compared to typical linear HCR, the nonlinear HCR and hyperbranched HCR were developed to program assembly systems with higher-order growth kinetics and amplification depth. [17][18][19] Apart from short linear DNA product, branched DNA products such as Y-shaped, X-shaped structures were obtained through CHA pathway, which could effectively reduce the signal leakage in some degree. [20][21][22] What's more, rational combination of HCR and CHA could achieve cascade amplification and enabled ultrasensitive homogeneous detection of target. [23][24][25][26][27] It is worthy noting that most of these assembly pathways were programmed to amplify DNA self-assembly has been developed as a kind of robust signal amplification strategy, but most of reported assembly pathways are programmed to amplify signal in one direction. Herein, based on mutual-activated cascade cycle of hybridization chain reaction (HCR) and catalytic hairpin assembly (CHA), a closed cycle circuit (CCC) based DNA machine is developed for sensitive logic operation and molecular recognition. Benefiting from the synergistically accelerated signal amplification, the closed cyclic DNA machine enabled the logic computing with strong and significant output signals even...