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Our primary concern is to obtain a clear characterization of which languages are recognizable by strictly local automata and which aren't. The view of SL2 automata as generators lets us do this by considering the characteristics of the tilings they build. Consider, for instance the situation in the top half of Figure 5, where there are two tilings u1σv1 and u2σv2 in which the symbol ‘σ' occurs. Clearly, after having built u1σ we had the choice of continuing with either v1 or with v2. We had the same choice after having built u2σ. Hence both of the tilings in the bottom half are constructable as well.
What this means for the strings, is that the question of whether we can extend a particular string to produce a longer string that is in the language depends only on the last symbol of that string.
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I want a proof for any NP complete problem
In Exercise 9 you showed that the recognition problem and universal recognition problem for SL2 are decidable. We can use the structure of Myhill graphs to show that other problems
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
Find the Regular Grammar for the following Regular Expression: a(a+b)*(ab*+ba*)b.
Define the following concept with an example: a. Ambiguity in CFG b. Push-Down Automata c. Turing Machine
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Automaton (NFA) (with ε-transitions) is a 5-tuple: (Q,Σ, δ, q 0 , F i where Q, Σ, q 0 and F are as in a DFA and T ⊆ Q × Q × (Σ ∪ {ε}). We must also modify the de?nitions of th
The path function δ : Q × Σ* → P(Q) is the extension of δ to strings: This just says that the path labeled ε from any given state q goes only to q itself (or rather never l
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
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