Decision problems, Theory of Computation

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 for SL2 are decidable as well. For example, Finiteness of SL2 languages is decidable, which is to say,
there is an algorithm that, given an SL2 automaton A, returns TRUE if L(A) is finite, FALSE otherwise.

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This close relationship between the SL2 languages and the recognizable languages lets us use some of what we know about SL 2 to discover properties of the recognizable languages.

Proof (sketch): Suppose L 1 and L 2 are recognizable. Then there are DFAs A 1 = (Q,Σ, T 1 , q 0 , F 1 ) and A 2 = (P,Σ, T 2 , p 0 , F 2 ) such that L 1 = L(A 1 ) and L 2 = L(

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 le

(c) Can you say that B is decidable? (d) If you somehow know that A is decidable, what can you say about B?

proof ogdens lemma .with example i am not able to undestand the meaning of distinguished position .