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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 2-factors to k-factors. We now have the possibility that the scanning window is actually longer than the augmented string. To accommodate that, we will permit factors of any length up to k as long as they start with ‘x' and end with ‘x' as well as k-factors which may or may not start with ‘x' or end with ‘x'.
So a strictly k-local automaton is just an alphabet and a set of stings of length k in which the ?rst symbol is either x or a symbol of the alphabet and the last is either x or a symbol of the alphabet, plus any number of strings of length no greater than k in which the ?rst and last symbol are x and x, respectively. In scanning strings that are shorter than k - 1, the automaton window will span the entire input (plus the beginning and end symbols). In that case, it will accept i? the sequence of symbols in the window is one of those short strings.
You should verify that this is a generalization of SL2 automata, that if k = 2 the de?nition of SLk automata is the same as the de?nition of SL2 automata.
(c) Can you say that B is decidable? (d) If you somehow know that A is decidable, what can you say about B?
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
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Automata and Compiler (1) [25 marks] Let N be the last two digits of your student number. Design a finite automaton that accepts the language of strings that end with the last f
designing DFA
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
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
Suppose G = (N, Σ, P, S) is a reduced grammar (we can certainly reduce G if we haven't already). Our algorithm is as follows: 1. Define maxrhs(G) to be the maximum length of the
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