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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.
The SL 2 languages are speci?ed with a set of 2-factors in Σ 2 (plus some factors in {?}Σ and some factors in Σ{?} distinguishing symbols that may occur at the beginning and en
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Find the Regular Grammar for the following Regular Expression: a(a+b)*(ab*+ba*)b.
The class of Strictly Local Languages (in general) is closed under • intersection but is not closed under • union • complement • concatenation • Kleene- and positive
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To see this, note that if there are any cycles in the Myhill graph of A then L(A) will be infinite, since any such cycle can be repeated arbitrarily many times. Conversely, if the
Another way of interpreting a strictly local automaton is as a generator: a mechanism for building strings which is restricted to building all and only the automaton as an inexh
Construct a PDA that accepts { x#y | x, y in {a, b}* such that x ? y and xi = yi for some i, 1 = i = min(|x|, |y|) }. For your PDA to work correctly it will need to be non-determin
The key thing about the Suffx Substitution Closure property is that it does not make any explicit reference to the automaton that recognizes the language. While the argument tha
Another way of representing a strictly 2-local automaton is with a Myhill graph. These are directed graphs in which the vertices are labeled with symbols from the input alphabet of
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