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This was one of the ?rst substantial theorems of Formal Language Theory. It's maybe not too surprising to us, as we have already seen a similar equivalence between LTO and SF. But it equates two very di?erent ways of specifying languages-ways that have almost nothing in common. The fact that these actually de?ne the same class of languages suggests that it is a "natural" class of some sort and not just an arbitrary class re?ecting the idiosyncrasies of the mechanisms we used. In wake Kleene's Theorem, the term Regular is uniformly used to denote both the languages that can be denoted by a regular expression and those that are recognized by FSA.
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
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
The path function δ : Q × Σ* → P(Q) is the extension of δ to strings: This just says that the path labeled ε from any given state q goes only to q itself (or rather never l
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
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
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The universe of strings is a very useful medium for the representation of information as long as there exists a function that provides the interpretation for the information carrie
#can you solve a problem of palindrome using turing machine with explanation and diagrams?
Give the Myhill graph of your automaton. (You may use a single node to represent the entire set of symbols of the English alphabet, another to represent the entire set of decima
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