Automated pattern detection: an algorithm for constructing optimally synchronizing multi-regular language filters

  • Authors:
  • Carl S. McTague;James P. Crutchfield

  • Affiliations:
  • Santa Fe Institute, Santa Fe, NM and Department of Mathematical Sciences, University of Cincinnati, Cincinnati, OH;Santa Fe Institute, Santa Fe, NM and Center for Computational Science & Engineering, University of California Davis, Davis, CA and Physics Department, University of California, Davis, Davis, CA

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2006

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Abstract

In the computational-mechanics structural analysis of one-dimensional cellular automata the following automata-theoretic analogue of the change-point problem from time series analysis arises: Given a string σ and a collection {Di} offinite automata, identify the regions of σ that belong to each Di and, in particular, the boundaries separating them. We present two methods for solving this multi-regular language filtering problem. The first, although providing the ideal solution, requires a stack, has a worst-case compute time that grows quadratically in σ's length and conditions its output at any point on arbitrarily long windows of future input. The second method is to algorithmically construct a finite transducer that approximates the first algorithm. In contrast to the stack-based algorithm, however, the transducer requires only a finite amount of memory, runs in linear time, and gives immediate output for each letter read; it is, moreover, the best possible finite-state approximation with these three features.