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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.
As de?ned the powerset construction builds a DFA with many states that can never be reached from Q′ 0 . Since they cannot be reached from Q′ 0 there is no path from Q′ 0 to a sta
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 s
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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)
Suppose A = (Σ, T) is an SL 2 automaton. Sketch an algorithm for recognizing L(A) by, in essence, implementing the automaton. Your algorithm should work with the particular automa
First model: Computer has a ?xed number of bits of storage. You will model this by limiting your program to a single ?xed-precision unsigned integer variable, e.g., a single one-by
LTO was the closure of LT under concatenation and Boolean operations which turned out to be identical to SF, the closure of the ?nite languages under union, concatenation and compl
We'll close our consideration of regular languages by looking at whether (certain) problems about regular languages are algorithmically decidable.
Theorem (Myhill-Nerode) A language L ⊆ Σ is recognizable iff ≡L partitions Σ* into ?nitely many Nerode equivalence classes. Proof: For the "only if" direction (that every recogn
One might assume that non-closure under concatenation would imply non closure under both Kleene- and positive closure, since the concatenation of a language with itself is included
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