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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.
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
Intuitively, closure of SL 2 under intersection is reasonably easy to see, particularly if one considers the Myhill graphs of the automata. Any path through both graphs will be a
Computer has a single LIFO stack containing ?xed precision unsigned integers (so each integer is subject to over?ow problems) but which has unbounded depth (so the stack itself nev
Can you say that B is decidable? If you somehow know that A is decidable, what can you say about B?
The Emptiness Problem is the problem of deciding if a given regular language is empty (= ∅). Theorem 4 (Emptiness) The Emptiness Problem for Regular Languages is decidable. P
LTO was the closure of LT under concatenation and Boolean operations which turned out to be identical to SF, the closure of the ?nite languages under union, concatenation and compl
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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
We will specify a computation of one of these automata by specifying the pair of the symbols that are in the window and the remainder of the string to the right of the window at ea
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