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We developed the idea of FSA by generalizing LTk transition graphs. Not surprisingly, then, every LTk transition graph is also the transition graph of a FSA (in fact a DFA)-the one in which the state set Q is just the set of nodes of the LTk transition graph. We get, as an immediate consequence, that every LT language (and, hence, every SL language and every ?nite language) is recognizable. In generalizing to arbitrary state sets, though, we have actually increased the power of our automata.
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We represented SLk automata as Myhill graphs, directed graphs in which the nodes were labeled with (k-1)-factors of alphabet symbols (along with a node labeled ‘?' and one labeled
what exactly is this and how is it implemented and how to prove its correctness, completeness...
The Myhill-Nerode Theorem provided us with an algorithm for minimizing DFAs. Moreover, the DFA the algorithm produces is unique up to isomorphism: every minimal DFA that recognizes
In Exercise 9 you showed that the recognition problem and universal recognition problem for SL2 are decidable. We can use the structure of Myhill graphs to show that other problems
Explain the Chomsky's classification of grammar
how to find whether the language is cfl or not?
Design a turing machine to compute x + y (x,y > 0) with x an y in unary, seperated by a # (descrition and genereal idea is needed ... no need for all TM moves)
Lemma 1 A string w ∈ Σ* is accepted by an LTk automaton iff w is the concatenation of the symbols labeling the edges of a path through the LTk transition graph of A from h?, ∅i to
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
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