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Let L 3 = {a i bc j | i, j ≥ 0}. Give a strictly 2-local automaton that recognizes L 3 . Use the construction of the proof to extend the automaton to one that recognizes L 3 . Gi
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
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
(c) Can you say that B is decidable? (d) If you somehow know that A is decidable, what can you say about B?
Claim Under the assumptions above, if there is an algorithm for checking a problem then there is an algorithm for solving the problem. Before going on, you should think a bit about
Let ? ={0,1} design a Turing machine that accepts L={0^m 1^m 2^m } show using Id that a string from the language is accepted & if not rejected .
The Universality Problem is the dual of the emptiness problem: is L(A) = Σ∗? It can be solved by minor variations of any one of the algorithms for Emptiness or (with a little le
The initial ID of the automaton given in Figure 3, running on input ‘aabbba' is (A, aabbba) The ID after the ?rst three transitions of the computation is (F, bba) The p
We got the class LT by taking the class SL and closing it under Boolean operations. We have observed that LT ⊆ Recog, so certainly any Boolean combination of LT languages will also
For every regular language there is a constant n depending only on L such that, for all strings x ∈ L if |x| ≥ n then there are strings u, v and w such that 1. x = uvw, 2. |u
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