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While the SL2 languages include some surprisingly complex languages, the strictly 2-local automata are, nevertheless, quite limited. In a strong sense, they are almost memoryless-the behavior of the automaton depends only on the most recent symbol it has read.
Certainly there are many languages of interest that are not SL2, that will require a more sophisticated algorithm than strictly 2-local automata.
One obvious way of extending the SL2 automata is to give them more memory. Consider, for instance, the language of algebraic expressions over decimal integer constants in which we permit negative constants, indicated by a pre?x ‘-'. Note that this is not the same as allowing ‘-' to be used as a unary operator. In the latter case we would allow any number of ‘-'s to occur in sequence (indicating nested negation), in the case in hand, we will allow ‘-'s to occur only singly (as either a subtraction operator or a leading negative sign) or in pairs (as a subtraction operator followed by a leading negative sign). We will still forbid embedded spaces and the use of ‘+' as a sign.
This is not an SL2 language. If we must permit ‘--' anywhere, then we would have to permit arbitrarily long sequences of ‘-'s. We can recognize this language, though, if we widen the automaton's scanning window to three symbols.
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We represented SLk automata as Myhill graphs, directed graphs in which the nodes were labeled with (k-1)-factors of alphabet symbols (along with a node labeled ‘?' and one labeled
DEGENERATE OF THE INITIAL SOLUTION
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
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Give DFA''s accepting the following languages over the alphabet {0,1}: i. The set of all strings beginning with a 1 that, when interpreted as a binary integer, is a multiple of 5.
Automaton (NFA) (with ε-transitions) is a 5-tuple: (Q,Σ, δ, q 0 , F i where Q, Σ, q 0 and F are as in a DFA and T ⊆ Q × Q × (Σ ∪ {ε}). We must also modify the de?nitions of th
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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