Reliable DNA computing requires a large pool of oligonucleotides that do not cross-hybridize. In this paper, we present a transformed algorithm to calculate the maximum weight of the 2-stem common subsequence of two DNA oligonucleotides. The result is the key part of the Gibbs free energy of the DNA cross-hybridized duplexes based on the nearest-neighbor model. The transformed algorithm preserves the physical data locality and hence is suitable for implementation using a systolic array. A novel hybrid architecture that consists of a general purpose microprocessor and a hardware accelerator for accelerating the discovery of DNA under thermodynamic constraints is designed, implemented and tested. Experimental results show that the hardware system provides more than 250X speed-up compared to a software only implementation.