Skip to main content
Open Access Publications from the University of California

Many roads to synchrony: Natural time scales and their algorithms

  • Author(s): James, RG
  • Mahoney, JR
  • Ellison, CJ
  • Crutchfield, JP
  • et al.

We consider two important time scales - the Markov and cryptic orders - that monitor how an observer synchronizes to a finitary stochastic process. We show how to compute these orders exactly and that they are most efficiently calculated from the ε-machine, a process's minimal unifilar model. Surprisingly, though the Markov order is a basic concept from stochastic process theory, it is not a probabilistic property of a process. Rather, it is a topological property and, moreover, it is not computable from any finite-state model other than the ε-machine. Via an exhaustive survey, we close by demonstrating that infinite Markov and infinite cryptic orders are a dominant feature in the space of finite-memory processes. We draw out the roles played in statistical mechanical spin systems by these two complementary length scales. © 2014 American Physical Society.

Many UC-authored scholarly publications are freely available on this site because of the UC Academic Senate's Open Access Policy. Let us know how this access is important for you.

Main Content
Current View