In this study, to substantially improve the runtimes of exact and approximate string matching algorithms, we propose a tribrid parallel method for bit-parallel algorithms such as the Shift-Or and Wu-Manber algorithms. Our underlying idea is to interpret bit-parallel algorithms as inclusive-scan operations, which allow these bit-parallel algorithms to run efficiently on a graphics processing unit (GPU); we achieve this speed-up here because inclusive-scan operations not only eliminate duplicate searches between threads but also realize a GPU-friendly memory access pattern that maximizes memory read/write throughput. To realize our ideas, we first define two binary operators and then present a proof regarding the associativity of these operators, which is necessary for the parallelization of the inclusive-scan operations. Finally, we integrate the inclusive-scan scheme into a previous segmentation-based scheme to maximize search throughput, identifying the best tradeoff point between synchronization cost and duplicate work. Through our experiments, we compared our proposed method with previous segmentation-based methods and indexing-based sequence aligners. For online string matching, our proposed method performed 6.7-16.7 times faster than previous methods, achieving a search throughput of up to 1.88 terabits per second (Tbps) on a GeForce GTX TITAN X GPU. We therefore conclude that our proposed method is quite effective for decreasing the runtimes of online string matching of short patterns.