DNA-based storage offers exceptional density and durability, but its scalability depends on efficiently synthesizing many strands in parallel under physical constraints. We study two complementary models capturing limitations arising from nucleotide availability and spatial interactions in large strand arrays.
First, we introduce complex synthesis sequences, a hybrid framework that bridges enzymatic synthesis, which permits strand-specific nucleotide additions, and photolithographic synthesis, which applies common additions across many strands. We characterize the achievable information rate through an analogue of the deletion ball, derive tight expressions for the maximal rate and its asymptotic behavior, and present a dynamic programming algorithm for computing an optimal synthesis sequence for known strands.
We then consider a two-dimensional array model motivated by optical and chemical coupling, in which strands follow a fixed global synthesis sequence and at most one strand per row may advance in each cycle. For two strands in a single row, we show that the laggard-first policy is asymptotically optimal among online policies without look-ahead, while one-symbol look-ahead yields a strict improvement in the binary case.
We further show that even globally optimal scheduling incurs an unavoidable expected overhead that grows linearly with strand length. These results are complemented by an offline dynamic programming algorithm and a constant-redundancy binary coding scheme with a deterministic worst-case synthesis-time guarantee. Together, the two works establish a unified framework for understanding the information-theoretic and scheduling limits of constrained DNA synthesis.