Constructing both basic and dynamic logic gates within a unified noise-driven system remains a challenge due to the lack of a comprehensive theoretical framework describing the underlying stochastic dynamics. In this work, we utilize the mean first-passage time theory to develop a robust theoretical framework for such systems. We propose a unique analytical criterion that allows for the determination of reliable parameter ranges without the need for extensive numerical simulations. This approach significantly reduces the time required for parameter scanning and enables more efficient identification of the operational stability of logic gates under noise. Validated by these analytical results, our numerical simulations uncover a key insight: by dissecting the types of logic signal input transitions, we identify the specific transition that predominantly determines the reliability of the logic gates. This discovery provides a criterion for the precise control of noise-driven dynamics, offering a comprehensive theoretical foundation for the design of flexible logic systems with improved reconfigurability and reliability.

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• Fluctuations & noise
• Stochastic processes
• Stochastic dynamical systems