Before revision:  We characterize this non-ideal behaviour in detail and characterize how the kinetic operation of the gate depends on the  toehold and adjacent domain lengths. In particular, we observe that, while the final output state is reached with high fidelity when both input strands are present, our simulations exhibit numerous long-lived transition paths from the initial input stateto the final output state .
After revision:  We characterize this non-ideal behaviour in detail and characterize how the kinetic operation of the gate depends on the toehold and adjacent domain length. Our gate displays excellent logical fidelity in three input states, and quite poor fidelity in the fourth input state. This illustrates how non-ideality can have very selective effects on fidelity. Simulations and detailed analysis such as those presented here provide molecular insights into strand displacement computation, that can be also be expected in chemical implementations .