Ternary Instantaneous Noise-Based Logic with Exponential Hilbert Space

Abstract

A tree-valued instantaneous noise-based logic with exponential Hilbert space is proposed. The third value is an uncertain bit value, which can be useful in artificial intelligence applications. The signal carrying the ternary universe has a significant advantage over the signal of the standard binary universe: its amplitude is never zero during any clock period. All known binary logic gates for exponential Hilbert space work for the binary sub-space in the ternary logic in the same way as they do in binary logic. This is useful when zeros cause problems in the exponential Hilbert space version of binary logic. Ternary logic is advantageous in various applications, including AI and natural language processing.