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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 right hand side of any production.
2. While maxrhs 3 we convert G to an equivalent reduced grammar G' with smaller maxrhs.
3. a) Choose a production A → α where is of maximal length in G.
b) Rewrite α as α1α2 where |α1| = |α1|/2 (largest integer ≤ |α1|/2) and |α2| = |α2|/2 (smallest integer ≥ |α2|/2)
c) Replace A -> α in P by A -> α1B and B -> α2
If we repeat step 3 for all productions of maximal length we create a grammar G' all of whose productions are of smaller length than maxrhs.
We can then apply the algorithm to G' and continue until we reach a grammar that has maxrhs ≤ 2.
The generalization of the interpretation of strictly local automata as generators is similar, in some respects, to the generalization of Myhill graphs. Again, the set of possible s
What is the arbwnememmsmdbdbfbfjmfksmjejfnfnfnnrndmnfjfjfnrnkrkfjfnfmkrjrbfbbfjfnfjruhrvrjkgktithhrbenfkiffnbr ki rnrjjdjrnrk bd n FBC..jcb?????????????????????????????????????????
To see this, note that if there are any cycles in the Myhill graph of A then L(A) will be infinite, since any such cycle can be repeated arbitrarily many times. Conversely, if the
A common approach in solving problems is to transform them to different problems, solve the new ones, and derive the solutions for the original problems from those for the new ones
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Theorem The class of ?nite languages is a proper subclass of SL. Note that the class of ?nite languages is closed under union and concatenation but SL is not closed under either. N
We will specify a computation of one of these automata by specifying the pair of the symbols that are in the window and the remainder of the string to the right of the window at ea
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