Read e-book online 2-Groups with normal noncyclic subgroups PDF

By Liman F.N.

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1 Blockade on the right: blockade of object Rules 2 and 4 are not recursive because they insert ULPS without o as an object of X. This absence of object in the resultant string prevents them from being applied again. These rules erase I n I. Therefore, their generative power is minimal, as the number of reaching levels is 2 and the number of forming sentences is also 2. 2 Blockade on the left: blockade of subject Rules 7 and 8 delete ( „ ] . Therefore, no other cut of s can be applied nor an insertion in its focal place.

X m } is the set of all words over V of length k. Clearly, £(A) = A. We define the morphisms h : (VI) {ci,c 2 ,.. ,cm,d1,d2, • • • ,d m })* —• V*, given by /i(a) = a, a 6 V, /i(cj-) = = Xi, 1 < i < m, fi h(di) = «e(K,) . i < * < m, and g : (V U {ci, c2, • • • ,cm, d1, d2,.. •, dm})* —> V*, given by g(a) — a, a E V, g(ci) = g{di) =e, 1 < i < m. Now we consider the regular language n n R=(\J V{Ci}V+{di}V) »=i U ([J V*{di}V+{Ci}V*). «=i We claim that hpek{L) =g(h-1{L)nR). Indeed, the regular language R assures that the following conditions are satisfied: - The strings in h~l(L) C\R are produced from those strings z in L for which there exists 1 < i < m such that both words x,- and £,(xi)R occur in z, separated by at least one symbol from V, whose inverse morphical images are the symbols c,- and di, respectively, or dj and Cj, respectively, for some j .

13. A. Tarski, The semantic conception of truth and the foundations of semantics, Philosophy and Phenomenological Research, 4 (1944), 341-376. 47 SOME REMARKS ON HAIRPIN A N D LOOP LANGUAGES JUAN CASTELLANOS Department of Artificial Intelligence Polytechnical University of Madrid 28660 Boadilla del Monte, Madrid, Spain E-mail: j c a s t e l l a n o s 6 f i . u p m . e s VICTOR MITRANA University of Bucharest, Faculty of Mathematics Str. ro We further investigate here the hairpin languages defined in [13] and introduce a similar type of languages, namely the loop languages, for which we study some decidability matters.

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2-Groups with normal noncyclic subgroups by Liman F.N.


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