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

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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 stringσ and a collection{ D i } of finite automata, identify the regions ofσ that belong to eachD i 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. © 2006 Elsevier B.V. All rights reserved.

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McTague, C. S., & Crutchfield, J. P. (2006). Automated pattern detection-An algorithm for constructing optimally synchronizing multi-regular language filters. Theoretical Computer Science, 359(1–3), 306–328. https://doi.org/10.1016/j.tcs.2006.05.002

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