Complex DNA Synthesis Sequences

DNA-based storage systems face a primary bottleneck in their parallel strand synthesis processes, affecting both economic viability and operational efficiency. Current methodologies predominantly employ either enzymatic DNA synthesis, permitting the addition of any nucleotide to individual strands per cycle, or photolithographic synthesis, facilitating the selective addition of a single nucleotide across multiple strands simultaneously. This research studies a theoretical hybrid framework combining both approaches, enabling the selection of a fixed number of nucleotides within each synthesis cycle. We introduce the term complex synthesis sequence to describe the nucleotide addition pattern and extend the concepts of subsequence and supersequence to enable standard sequences to be subsequences of complex synthesis sequences. We extend Lenz et al.'s definition of information rate and use an analog of the deletion ball to derive expressions for the maximal information rate obtainable in this model. We develop an algorithm to determine the optimal synthesis sequence in this model for known strands, show that the solution is analogous to finding an SCS, and derive the required dynamic programming algorithm to solve it.