# Abstract machines and grammars by Walter J Savitch

By Walter J Savitch

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This e-book constitutes the refereed court cases of the eleventh foreign Workshop on summary nation Machines, ASM 2004, held in Lutherstadt Wittenberg, Germany, in may possibly 2004. The 12 revised complete examine papers provided including four invited papers have been rigorously reviewed and chosen for inclusion within the ebook.

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So there are an infinite number of strings in L, namely, the uvi wxi y. Thus (1) is shown. Next we show (2). Suppose L is infinite. We must show that L n F is not empty. Since L is infinite, it follows that there are arbitrarily long strings in L. So there must be some string z in L such that length(z) > k. Now if length (z) ~ 2k, then z is in F. Thus z is L n F and (2) is true. Unfortunately, all we know is that length(z) > k. It could be true that length(z) > 2k. Assume the worst, namely, that length(z) > 2k.

What is L (G)? Gas in 9. CHAPTER 2. CONTEXT-FREE GRAMMARS 29 11. 14 to find a cfg in Chomsky normal form that is equivalent to G. a. G=(N, T,P,S)whereN={S,A,B,C}, T={a,b,c}. P = {S-ABC, A-aA, A-a, B-bB, B-b, C-cC, C-c}. b. G = (N, T, P, S) where N = {S, A, B, C}, T= {a, b, c}. P = {S-ABC, C-A, A-a, B-b, C-c}. c. Gas in 9. 12. For each G in 11, describe L ( G ) . 13. Give an algorithm that will determine for any cfg G whether or not L (G ) is empty, that is, whether or not it is possible to generate any terminal string from the start symbol.

This machine will accept those strings of zeros and ones which contain an odd number of ones and rejects those strings of zeros and ones which contain an even number of ones. In terms of the mathematical formalism, this machine is a five-tuple (S, :E, 8, s, Y) where S = {