Download 600 Essential Words for the TOEIC - 3rd Edition by Lin Lougheed Ed.D. PDF

By Lin Lougheed Ed.D.

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The syntactic monoid congruence /-LT of a EX-language T is a congruence of the monoid of EX-contexts which is defined so that for any p, q E Ct( E, X), P/-LTq iff ("It E T:r;(X))(Vr E Ct(E, X))[t· p. rET {:} t· q. rET]. The syntactic monoid of T is defined in [Th084] as the quotient monoid Ct(E,X)//-LT' In [Sa183] it was shown that the syntactic monoid of any EXlanguage T is isomorphic to the translation monoid of the syntactic algebra of T. This means that T is recognizable iff its syntactic monoid is finite.

Tree languages OI-generated (IO-generated) by contextfree tree grammars are called aI-tree languages (la-tree languages). It is not hard to show that the OI-tree languages are exactly the context-free tree languages. Tree Languages 37 Engelfriet and Schmidt in [EnS77 /78] give fixed point characterizations for OI and 10 tree languages. Their basic operations are the OI and 10 tree language substitutions.

P. (q) = uez and yd(s) = x, then yd(t) = uvxyz and yd(s· pk . q) = uvkxykz for all k ~ 0, and (2) that if yd(t) = wand 19(w) = n, then hg(t) ~ log2n. 2 simply generalizes the usual proof of the Pumping Lemma for OF languages. 8. The intersection of a CF language L(~ X*) and a regular language R(~ X*) is again a CF language. This is usually proved by constructing from a pushdown automaton recognizing L and a finite automaton recognizing R a new pushdown automaton which recognizes L n R. However, the fact follows also very simply from the results of this section and the observation that if L = yd(T) , then L n R = yd(T n yd-l(R)).

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