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So we have that every language that can be constructed from SL languages using Boolean operations and concatenation (that is, every language in LTO) is recognizable but there are recognizable languages that cannot be constructed in this way. The one fundamental operation that LTO was not closed under was Kleene closure. It's worth asking, then, how the class of recognizable languages fairs under Kleene closure.
Suppose A = (Σ, T) is an SL 2 automaton. Sketch an algorithm for recognizing L(A) by, in essence, implementing the automaton. Your algorithm should work with the particular automa
Paths leading to regions B, C and E are paths which have not yet seen aa. Those leading to region B and E end in a, with those leading to E having seen ba and those leading to B no
Can you say that B is decidable? If you somehow know that A is decidable, what can you say about B?
how to prove he extended transition function is derived from part 2 and 3
Sketch an algorithm for the universal recognition problem for SL 2 . This takes an automaton and a string and returns TRUE if the string is accepted by the automaton, FALSE otherwi
examples of decidable problems
Exercise Show, using Suffix Substitution Closure, that L 3 . L 3 ∈ SL 2 . Explain how it can be the case that L 3 . L 3 ∈ SL 2 , while L 3 . L 3 ⊆ L + 3 and L + 3 ∈ SL
We can then specify any language in the class of languages by specifying a particular automaton in the class of automata. We do that by specifying values for the parameters of the
One of the first issues to resolve, when exploring any mechanism for defining languages is the question of how to go about constructing instances of the mechanism which define part
While the SL 2 languages include some surprisingly complex languages, the strictly 2-local automata are, nevertheless, quite limited. In a strong sense, they are almost memoryless
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