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By Gregory Karpilovsky
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Example text
In a series of papers (see [2,6,7]) the problem of finding sets of DNA sequences which are unlikely to lead to "bad" hybridizations is considered. Some algebraic properties of sets formed by such sequences are investigated in [8]. On the other hand, these molecules which may form a hairpin structure have been used as the basic feature of a new computational model reported in [17], where an instance of the 3-SAT problem has been solved by a DNA-algorithm in which the second phase is mainly based on the elimination of hairpin structured molecules.
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 .
However, Catalan always uses infinitive. 1 Recursive rules on the right: multiple object insertion Rules 1 and 3, which insert ULPS with the group vo as an object of X, have the same generative result. If we take a terminal string obtained by means of rule 1 -st; I (s'v'o')i0- as an X structure and we apply the rule again, then the result is: x = sv I (sVLoO, y = s"v"o", Q{x,y) = sv I (sV I E x a m p l e 14 x = El gat viu on en Joan juga # a tennis {s"v"o")t0)lo y = El conductor te tres flors x = The cat l i v e s where John plays # t e n n i s y = The d r i v e r has t h r e e flowers 0(x,y) = El gat viu on Joan juga a que el conductor te tres flors Q(x,t/) = The cat l i v e s where John p l a y s t h e d r i v e r has t h r e e flowers Rules 1 and 3 have the same results if in 3 all the ULPS accomplish that q = l(v).