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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.
implementation of operator precedence grammer
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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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Normal forms are important because they give us a 'standard' way of rewriting and allow us to compare two apparently different grammars G1 and G2. The two grammars can be shown to
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