A space-time tradeoff for implementing a function with master equation dynamics.

ABSTRACT: Master equations are commonly used to model the dynamics of physical systems, including systems that implement single-valued functions like a computer's update step. However, many such functions cannot be implemented by any master equation, even approximately, which raises the question of how they can occur in the real world. Here we show how any function over some "visible" states can be implemented with master equation dynamics-if the dynamics exploits additional, "hidden" states at intermediate times. We also show that any master equation implementing a function can be decomposed into a sequence of "hidden" timesteps, demarcated by changes in what state-to-state transitions have nonzero probability. In many real-world situations there is a cost both for more hidden states and for more h

SUBMITTER: Wolpert DH 

PROVIDER: S-EPMC6465315 | biostudies-literature | 2019 Apr

REPOSITORIES: biostudies-literature