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We have now de?ned classes of k-local languages for all k ≥ 2. Together, these classes form the Strictly Local Languages in general.
De?nition (Strictly Local Languages) A language L is strictly local (L ∈ SL) iff it is strictly k-local for some k.
Again, we can generalize the work we have done so far to establish properties of the class of strictly local languages as a whole.
Theorem 3 ((General) Suffix Substitution Closure) A language L is strictly local iff there is some k such that, for all strings u1, v1, u2, and v2 in Σ* and all strings x in Σk-1 :
u1xv1 ∈ L and u2xv2 ∈ L ⇒ u1xv2 ∈ L.
We'll close our consideration of regular languages by looking at whether (certain) problems about regular languages are algorithmically decidable.
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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
s->0A0|1B1|BB A->C B->S|A C->S|null find useless symbol?
A.(A+C)=A
A finite, nonempty ordered set will be called an alphabet if its elements are symbols, or characters. A finite sequence of symbols from a given alphabet will be called a string ove
Theorem The class of recognizable languages is closed under Boolean operations. The construction of the proof of Lemma 3 gives us a DFA that keeps track of whether or not a give
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While the SL 2 languages include some surprisingly complex languages, the strictly 2-local automata are, nevertheless, quite limited. In a strong sense, they are almost memoryless
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