# Download Words, Semigroups, Transductions by S. Yu, Gh Paun, Masami Ito, Gabriel Thierrin, Gheorghe Paun, PDF

By S. Yu, Gh Paun, Masami Ito, Gabriel Thierrin, Gheorghe Paun, Sheng Yu

Researchers in arithmetic and desktop technology; this is often a good selection of papers facing combinatorics on phrases, codes, semigroups, automata, languages, molecular computing, transducers, logics, etc., concerning the amazing paintings of Gabriel Thierrin. This quantity is in honor of Professor Thierrin at the get together of his eightieth birthday.

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**Extra resources for Words, Semigroups, Transductions**

**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).