  In the computational-mechanics structural analysis of one-dimensional
cellular automata the following automata-theoretic analogue of the
\emph{change-point problem} from time series analysis arises: \emph{Given a
string $\sigma$ and a collection $\{\mc{D}_i\}$ of finite automata, identify
the regions of $\sigma$ that belong to each $\mc{D}_i$ and, in particular, the
boundaries separating them.} We present two methods for solving this
\emph{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 $\sigma$'s length and conditions its output at any point on
arbitrarily long windows of future input. The second method is to
algorithmically construct a 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.
