Systems and methods for capturing desired interactions and non-interactions of a set of strands (e.g., DNA strands, RNA strands) that may be used in various technological applications, including DNA molecular probes used in medical diagnostics, forensics, microbial ecology, molecular computation, DNA origami, and numerous other applications. Given a nucleic acid system with a certain defined binding pattern, the implementations of the present disclosure automatically generate nucleotide sequences that achieve the intended binding pattern and not other binding patterns, subject to miscellaneous other constraints of the system. Advantageously, given nucleotides i and j, the implementations of the present disclosure consider the binding behavior only in a limited neighborhood of nucleotides surrounding each nucleotide in their respective strands, rather than the binding behavior of whole assignment of which they are a part. These features provide a time-efficient and incremental algorithm that is suitable for numerous practical applications.