DNA is a reliable biomolecule with which to build molecular computation systems. In particular, DNA logic circuits (diffusion-based) have shown good performance regarding scalability and correctness of computation. However, previous architectures of DNA logic circuits have two limitations. First, the speed of computation is slow, often requiring hours to compute a simple function. Second, the circuits are of high complexity regarding the number of DNA strands. Here, we introduce an architecture of DNA logic circuits based on single-stranded logic gates using strand-displacing DNA polymerase. The logic gates consist of only single DNA strands, which largely reduces leakage reactions and signal restoration steps such that the circuits are improved in regard to both speed of computation and the number of DNA strands needed. Large-scale logic circuits can be constructed from the gates by simple cascading strategies. In particular, we have demonstrated a fast and compact logic circuit that computes the square-root function of four-bit input numbers.