Inspired by naturally occurring protein dimerization networks, in which a set of proteins interact with each other to achieve highly complex input-output behaviors, we demonstrate here a fully synthetic DNA-based dimerization network that enables highly programmable input-output computations. Our DNA-based dimerization network consists of DNA oligonucleotide monomers modified with reactive moieties that can covalently bond with each other to form dimer outputs in an all-to-all or many-to-many fashion. By designing DNA-based input strands that can specifically sequester DNA monomers, we can control the size of the reaction network and thus fine-tune the yield of each DNA dimer output in a predictable manner. Thanks to the programmability and specificity of DNA-DNA interactions, we show that this approach can be used to control the yield of different dimer outputs using different inputs. The approach is also versatile and we demonstrate dimerization networks based on two distinct covalent reactions: thiol-disulfide and strain-promoted azide-alkyne cycloaddition (SPAAC) reactions. Finally, we show here that the DNA-based dimerization network can be used to control the yield of a functional dimer output, ultimately controlling the assembly and disassembly of DNA nanostructures. The covalent dynamic DNA networks shown here provide a way to convert multiple inputs into programmable outputs that can control a broader range of functions, including ones that mimic those of living cells.