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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 σ_{2}, . . . , σ_{k}, σ_{k+1} to be placed over the last k-1 symbols of a tile labeled σ_{1}, σ_{2}, . . . , σ_{k}. 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'.
s-> AACD A-> aAb/e C->aC/a D-> aDa/bDb/e
Both L 1 and L 2 are SL 2 . (You should verify this by thinking about what the automata look like.) We claim that L 1 ∪ L 2 ∈ SL 2 . To see this, suppose, by way of con
Automaton (NFA) (with ε-transitions) is a 5-tuple: (Q,Σ, δ, q 0 , F i where Q, Σ, q 0 and F are as in a DFA and T ⊆ Q × Q × (Σ ∪ {ε}). We must also modify the de?nitions of th
Our primary concern is to obtain a clear characterization of which languages are recognizable by strictly local automata and which aren't. The view of SL2 automata as generators le
Applying the pumping lemma is not fundamentally di?erent than applying (general) su?x substitution closure or the non-counting property. The pumping lemma is a little more complica
Theorem The class of ?nite languages is a proper subclass of SL. Note that the class of ?nite languages is closed under union and concatenation but SL is not closed under either. N
examples of decidable problems
Differentiate between DFA and NFA. Convert the following Regular Expression into DFA. (0+1)*(01*+10*)*(0+1)*. Also write a regular grammar for this DFA.
Can v find the given number is palindrome or not using turing machine
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