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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'.
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This close relationship between the SL2 languages and the recognizable languages lets us use some of what we know about SL 2 to discover properties of the recognizable languages.
We will specify a computation of one of these automata by specifying the pair of the symbols that are in the window and the remainder of the string to the right of the window at ea
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Given any NFA A, we will construct a regular expression denoting L(A) by means of an expression graph, a generalization of NFA transition graphs in which the edges are labeled with
The k-local Myhill graphs provide an easy means to generalize the suffix substitution closure property for the strictly k-local languages. Lemma (k-Local Suffix Substitution Clo
Paths leading to regions B, C and E are paths which have not yet seen aa. Those leading to region B and E end in a, with those leading to E having seen ba and those leading to B no
The Universality Problem is the dual of the emptiness problem: is L(A) = Σ∗? It can be solved by minor variations of any one of the algorithms for Emptiness or (with a little le
The project 2 involves completing and modifying the C++ program that evaluates statements of an expression language contained in the Expression Interpreter that interprets fully pa
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