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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 particular, given languages. Towards that end, note that a strictly 2-local automaton can require a particular symbol to appear at the beginning or end of the string and it can permit particular pairs of symbols to occur in the interior of the string but, in general, it can't require an arbitrary pair of symbols to occur in the interior of the string. Consider, for example the language:
This is just the set of all strings over {a, b} in which the sequence ‘ab' occurs at least once. Since the string aabaa is in L1, any strictly 2-local automaton will have to include at least the pairs:
fia, aa, ab, ba, afi.
But then the string aaaaa will also be accepted, using just the first two and the last one of these pairs. Roughly, as long as we have to permit other pairs starting with ‘a' we cannot require ‘ab' to occur.
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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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Give the Myhill graph of your automaton. (You may use a single node to represent the entire set of symbols of the English alphabet, another to represent the entire set of decima
The upper string r ∈ Q+ is the sequence of states visited by the automaton as it scans the lower string w ∈ Σ*. We will refer to this string over Q as the run of A on w. The automa
Let G be a graph with n > 2 vertices with (n2 - 3n + 4)/2 edges. Prove that G is connected.
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We'll close our consideration of regular languages by looking at whether (certain) problems about regular languages are algorithmically decidable.
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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