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We have now de?ned classes of k-local languages for all k ≥ 2. Together, these classes form the Strictly Local Languages in general.
De?nition (Strictly Local Languages) A language L is strictly local (L ∈ SL) iff it is strictly k-local for some k.
Again, we can generalize the work we have done so far to establish properties of the class of strictly local languages as a whole.
Theorem 3 ((General) Suffix Substitution Closure) A language L is strictly local iff there is some k such that, for all strings u1, v1, u2, and v2 in Σ* and all strings x in Σk-1 :
u1xv1 ∈ L and u2xv2 ∈ L ⇒ u1xv2 ∈ L.
If the first three words are the boys down,what are the last three words??
The computation of an SL 2 automaton A = ( Σ, T) on a string w is the maximal sequence of IDs in which each sequential pair of IDs is related by |- A and which starts with the in
Consider a water bottle vending machine as a finite–state automaton. This machine is designed to accept coins of Rs. 2 and 5 only. It dispenses a single water bottle as soon as 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
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
Strictly 2-local automata are based on lookup tables that are sets of 2-factors, the pairs of adjacent symbols which are permitted to occur in a word. To generalize, we extend the
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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.
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