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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.
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Our primary concern is to obtain a clear characterization of which languages are recognizable by strictly local automata and which aren't. The view of SL2 automata as generators le
Trees and Graphs Overview: The problems for this assignment should be written up in a Mircosoft Word document. A scanned hand written file for the diagrams is also fine. Be
The path function δ : Q × Σ* → P(Q) is the extension of δ to strings: This just says that the path labeled ε from any given state q goes only to q itself (or rather never l
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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
Differentiate between DFA and NFA. Convert the following Regular Expression into DFA. (0+1)*(01*+10*)*(0+1)*. Also write a regular grammar for this DFA.
spam messages h= 98%, m= 90%, l= 80% non spam h=12%, m = 8%, l= 5% The organization estimates that 75% of all messages it receives are spam messages. If the cost of not blocking a
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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