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Let there L1 and L2 . We show that L1 ∩ L2 is CFG . Let M1 be a decider for L1 and M2 be a decider for L2 . Consider a 2-tape TM M: "On input x: 1. copy x on the second
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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 langu
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. N
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The fundamental idea of strictly local languages is that they are speci?ed solely in terms of the blocks of consecutive symbols that occur in a word. We'll start by considering lan
The SL 2 languages are speci?ed with a set of 2-factors in Σ 2 (plus some factors in {?}Σ and some factors in Σ{?} distinguishing symbols that may occur at the beginning and en
Can you say that B is decidable? If you somehow know that A is decidable, what can you say about B?
The fact that the Recognition Problem is decidable gives us another algorithm for deciding Emptiness. The pumping lemma tells us that if every string x ∈ L(A) which has length grea
All that distinguishes the de?nition of the class of Regular languages from that of the class of Star-Free languages is that the former is closed under Kleene closure while the lat
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