Abstract: Methods and systems for encoding digital information in nucleic acid (e.g., deoxyribonucleic acid) molecules without base-by-base synthesis, by encoding bit-value information in the presence or absence of unique nucleic acid sequences within a pool. Described in this specification are methods for enumerating all elements of a combinatorial search space and searching for a solution, where a solution is described by constraints over categorical variables. A set of variables are mapped to an identifier nucleic acid sequence, the search space to a set of identifiers, and a constraint to a chemical method that selects a subset of identifiers satisfying the constraint.