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The generalization of the interpretation of strictly local automata as generators is similar, in some respects, to the generalization of Myhill graphs. Again, the set of possible symbols that may appear at any given point depends only on the previous k - 1 symbols. Here this is realized by taking the factors to be tiles and allowing a tile labeled σ2, . . . , σk, σk+1 to be placed over the last k-1 symbols of a tile labeled σ1, σ2, . . . , σk. Again, the process starts with a tile labeled 'x ' and ends when a tile labeled ' x' is placed. Strings of length less than k - 1 are generated with a single tile.
Note that there is a sense in which this mechanism is the dual of the k-local Myhill graphs. In the graphs, the vertices are labeled with the pre?x of the factors in the automaton and the edges are labeled with the last symbol of the label of the node the edge is incident to. It is those edge labels that call out the string being recognized and the initial k - 1 positions of the string label the edges incident from ‘x'. Here it is the exposed symbols that call out the string being generated and these are the initial symbols of the tiles. And the ?nal k -1 symbols of the string are the symbols labeling the last tile, the one labeled with ‘x'.
LTO was the closure of LT under concatenation and Boolean operations which turned out to be identical to SF, the closure of the ?nite languages under union, concatenation and compl
Another way of interpreting a strictly local automaton is as a generator: a mechanism for building strings which is restricted to building all and only the automaton as an inexh
Myhill graphs also generalize to the SLk case. The k-factors, however, cannot simply denote edges. Rather the string σ 1 σ 2 ....... σ k-1 σ k asserts, in essence, that if we hav
If the first three words are the boys down,what are the last three words??
To see this, note that if there are any cycles in the Myhill graph of A then L(A) will be infinite, since any such cycle can be repeated arbitrarily many times. Conversely, if the
20*2
Another way of representing a strictly 2-local automaton is with a Myhill graph. These are directed graphs in which the vertices are labeled with symbols from the input alphabet of
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