New noise-based logic representations to avoid some problems with time complexity

Abstract: Instantaneous noise-based logic can avoid time-averaging, which implies significant potential for low-power parallel operations in beyond-Moore-law-chips. However, the universe (uniform superposition) will be zero with high probability (non-zero with exponentially low probability) in the random-telegraph-wave representation thus the operations with the universe would require exponential time-complexity. To fix this deficiency, we modify the amplitudes of the signals of the L and H states and achieve an exponential speedup compared to the old situation. Another improvement concerns the identification of a single product (hyperspace) state. We introduce a time shifted noise-based logic, which is constructed by shifting each reference signal with a small time delay. This modification implies an exponential speedup of single hyperspace vector identification compared to the former case and it requires the same, O(N) complexity as in quantum computing.