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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. Nevertheless, this does not contradict the fact that every ?nite language is SLk, for some k. All it says is that the counterexamples that establish non-closure of SL under union and concatenation must involve non-?nite languages. (You should verify the fact that they do.)
Find the Regular Grammar for the following Regular Expression: a(a+b)*(ab*+ba*)b.
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
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
When we say "solved algorithmically" we are not asking about a speci?c programming language, in fact one of the theorems in computability is that essentially all reasonable program
The Emptiness Problem is the problem of deciding if a given regular language is empty (= ∅). Theorem 4 (Emptiness) The Emptiness Problem for Regular Languages is decidable. P
turing machine
how to prove he extended transition function is derived from part 2 and 3
As we are primarily concerned with questions of what is and what is not computable relative to some particular model of computation, we will usually base our explorations of langua
We'll close our consideration of regular languages by looking at whether (certain) problems about regular languages are algorithmically decidable.
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
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