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By Yordanov I.

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1. a is ambiguity preserving by providing the production S ~ aC with two different indexes. 1. c. One may say that in this way syntactical ambiguity is replaced by semantical ambiguity. With our adaptation of the standard method this replacement of ambiguity is not necessary. 52 A ~ C B / ~ C a c a a. Decrease of ambiguity A C a B c C a a•C a• a• c c C1 c c C2 c b. > A C a B c C a c c c. 1~ Transformations to Greibach normal form. The following algorithm will produce a left covering granmmr in GNF for a proper NLR grammar.

Hc c 29 Without further restrictions on F we can not, without further knowledge of G and G', compare and . Grammar functor F can be restricted to the HOMsets of S(G'). Let ~,8c V'* then the HOM-set of (~,8) is denoted by S(G')(~,~) and the restriction of F to this HOM-set is denoted by F(~,8) : S(G')(e,~) + S(G)(F(~), F(8)). It is fairly easy to compare grammar functors and covers. In the case of a cover we are only interested in the relation between the parse relations of G' and G.

X n ~ N*Z I x0 ~ x,~ l ' " l X~n' ~i ~ V*, I ~ i ~ n}, a~d for c • Z, c~(c) : {c}. In the following theorem some properties of chains are listed. 10. b. 1. Let G = (N,Z,P,S) be a proper CFG. (i) For each X • V, CH(X) is a regular set. (ii) Grammar G is NLR if and only if, for all X • V, CH(X) is a finite set. (iii) Grammar G is in quasi-GNF if and only if, for each X • V and for each ~ • CH(X), Proof. (i) If X • Z then CH(X) = {X}, which is a regular set. Assume X • N. We con- struct a (right) regular grammar G X = (Nx,%x,Px,[X]) such that L(Gx) = CH(X).

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All about file IO in C++ by Yordanov I.

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