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The computation of an SL2 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 initial con?guration of A on w: (p1,w1), where p1 . w1 = ?w?.
Since w is ?nite, the computation of A on w will be ?nite. Since it is required to be maximal, the last ID will be one that does not directly compute any other ID. This will either be of the form (σiσj) , wii where σiσj ∈ T, or of the form (σn?, ε), in which σn? ∈ T but all the input has been consumed. In the ?rst case we will say that the computation is rejecting (or that it crashes). In the second we will say that it is accepting. Note that we have adopted the convention that the automaton halts with FALSE as soon as it encounters a pair of symbols that are not in T.
These assumptions hold for addition, for instance. Every instance of addition has a unique solution. Each instance is a pair of numbers and the possible solutions include any third
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
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Intuitively, closure of SL 2 under intersection is reasonably easy to see, particularly if one considers the Myhill graphs of the automata. Any path through both graphs will be a
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Prove xy+yz+ýz=xy+z
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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
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