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We now add an additional degree of non-determinism and allow transitions that can be taken independent of the input-ε-transitions.
Here whenever the automaton is in state 1 it may make a transition to state 3 without consuming any input. Similarly, if it is in state 0 it may make such a transition to state 2. The advantage of such transitions is that they allow one to build NFAs in pieces, with each piece handling some portion of the language, and then splice the pieces together to form an automaton handling the entire language. To accommodate these transitions we need to modify the type of the transition relation to allow edges labeled ε.
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Exercise: Give a construction that converts a strictly 2-local automaton for a language L into one that recognizes the language L r . Justify the correctness of your construction.
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It is not hard to see that ε-transitions do not add to the accepting power of the model. The underlying idea is that whenever an ID (q, σ v) directly computes another (p, v) via
We will assume that the string has been augmented by marking the beginning and the end with the symbols ‘?' and ‘?' respectively and that these symbols do not occur in the input al
The generalization of the interpretation of strictly local automata as generators is similar, in some respects, to the generalization of Myhill graphs. Again, the set of possible s
Lemma 1 A string w ∈ Σ* is accepted by an LTk automaton iff w is the concatenation of the symbols labeling the edges of a path through the LTk transition graph of A from h?, ∅i to
Since the signi?cance of the states represented by the nodes of these transition graphs is arbitrary, we will allow ourselves to use any ?nite set (such as {A,B,C,D,E, F,G,H} or ev
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