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Abstract Applications of RNA-based molecular logic have been hampered by sequence constraints imposed on the input and output of the circuits. Here we show that the sequence constraints can be substantially reduced by appropriately encoded multi-arm junctions of single-stranded RNA structures. To conditionally activate RNA translation, we integrated multi-arm junctions, self-assembled upstream of a regulated gene and designed to unfold sequentially in response to different RNA inputs, with motifs of loop-initiated RNA activators that function independently of the sequence of the input RNAs and that reduce interference with the output gene. We used the integrated RNA system and sequence-independent input RNAs to execute two-input and three-input OR and AND logic in Escherichia coli , and designed paper-based cell-free colourimetric assays that accurately identified two human immunodeficiency virus (HIV) subtypes (by executing OR logic) in amplified synthetic HIV RNA as well as severe acute respiratory syndrome coronavirus-2 (via two-input AND logic) in amplified RNA from saliva samples. The sequence-independent molecular logic enabled by the integration of multi-arm junction RNAs with motifs for loop-initiated RNA activators may be broadly applicable in biotechnology.