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Binary Equality Set Is Generated By Two Words
, 2002
"... We show that the equality set Eq(g; h) of two nonperiodic binary morphisms g; h : is generated by at most two words. If the rank of Eq(g; h) = f; g is two, then and start and end with dierent letters. This in particular implies that any binary language has a test set of cardinality at most t ..."
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We show that the equality set Eq(g; h) of two nonperiodic binary morphisms g; h : is generated by at most two words. If the rank of Eq(g; h) = f; g is two, then and start and end with dierent letters. This in particular implies that any binary language has a test set of cardinality at most two. 1
Many Aspects of Defect Theorems
 Theor. Comput. Sci
"... We give a survey and a unified presentation of the defect theorem, its generalizations and recent aspects of interest. In its basic form the defect theorem states that if a set of n words satisfies a nontrivial relation, then these words can be expressed simultaneously as products of at most n 1 wor ..."
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We give a survey and a unified presentation of the defect theorem, its generalizations and recent aspects of interest. In its basic form the defect theorem states that if a set of n words satisfies a nontrivial relation, then these words can be expressed simultaneously as products of at most n 1 words. In other words, dependency of words causes a defect effect. There does not exist just one defect theorem, but several ones depending on the restrictions that are put to the n 1 words. The defect theorem is closely related to equations of words, and in this way to the compactness theorem for systems of word equations.
Defect theorems with compatibility relation
, 2006
"... We consider words together with a compatibility relation induced by a relation on letters. Unique factorization with respect to two arbitrary word relations R and S defines the (R, S)freeness of the semigroup considered. We generalize the stability theorem of Schützenberger and Tilson’s closure res ..."
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We consider words together with a compatibility relation induced by a relation on letters. Unique factorization with respect to two arbitrary word relations R and S defines the (R, S)freeness of the semigroup considered. We generalize the stability theorem of Schützenberger and Tilson’s closure result for (R, S)free semigroups. The inner and the outer (R, S)unique factorization hull and the (R, S)free hull of a set of words are introduced and we show how they can be computed. We prove that the (R, S)unique factorization hulls possess a defect effect, which implies a variant of a cumulative defect theorem of word semigroups. In addition, a defect theorem of partial words is proved as a corollary.
Defect Theorems for Trees
 Proceedings of the "8th International Conference Automata and Formal Languages", Salg'otarj'an (Hungary
, 1996
"... We generalize different notions of a rank of a set of words to sets of trees. We prove that almost all of those ranks can be used to formulate a defect theorem. However, as we show, the prefix rank forms an exception. ..."
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We generalize different notions of a rank of a set of words to sets of trees. We prove that almost all of those ranks can be used to formulate a defect theorem. However, as we show, the prefix rank forms an exception.
Liste De Publications
, 1996
"... Schutzenberger. Codes et sousmonoides poss'edant des mots neutres. In Theoretical Computer Science, volume 48 of Lecture Notes in Computer Science, pages 2744. Springer Verlag, 1977. [72] D. Perrin and M.P. Schutzenberger. Un probl`eme 'el'ementaire de la th'eorie de l'information. In Th'eorie d ..."
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Schutzenberger. Codes et sousmonoides poss'edant des mots neutres. In Theoretical Computer Science, volume 48 of Lecture Notes in Computer Science, pages 2744. Springer Verlag, 1977. [72] D. Perrin and M.P. Schutzenberger. Un probl`eme 'el'ementaire de la th'eorie de l'information. In Th'eorie de l'information, pages 249260. CNRS, 1977. [73] D. Perrin and M.P. Schutzenberger. A conjecture on sets of differences of integer pairs. J. Comb. Theory, Ser. B, 30:9193, 1981. [74] D. Perrin and M.P. Schutzenberger. Synchronizing words and automata and the road coloring problem. In Peter Walters, editor, Symbolic Dynamics and its Applications, pages 295318. American Mathematical Society, 1992. Contemporary Mathematics, vol. 135. [75] D. Perrin and G. Viennot. A note on shuffle algebras. manuscrit non publi'e, 1980. [76] Dominique Perrin. Automata on infinite words. In IFIP World Computer Congress<F
CHAPTER 1 Words
"... Introduction This chapter contains the main definitions used in the rest of the book. It also presents some basic results about words that are of constant use in the sequel. In the first section are defined words, free monoids, and some terms about words, such as length and factors. Section 1.2 is ..."
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Introduction This chapter contains the main definitions used in the rest of the book. It also presents some basic results about words that are of constant use in the sequel. In the first section are defined words, free monoids, and some terms about words, such as length and factors. Section 1.2 is devoted to submonoids and to morphism of free monoids, one of the basic tools for words. Many of the proofs of properties of words involve a substitution from the alphabet into words over another alphabet, which is just the definition of a morphism of free monoids. A nontrivial result called the defect theorem is proved. The theorem asserts that if a relation exists among words in a set, those words can be written on a smaller alphabet. This is a weak counterpart for free monoids of the NielsenSchreier theorem for subgroups of a free group. In Section 1.3 the definition of conjugate words is given, together with some equivalent characterizations. Also defined are<F2
The Acw Style
"... Contents 29 The acw style 1 29.0 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 29.1 Page Layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 29.2 Proclamations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 29.2.1 Theorems etc. . . . . . . . . . ..."
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Contents 29 The acw style 1 29.0 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 29.1 Page Layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 29.2 Proclamations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 29.2.1 Theorems etc. . . . . . . . . . . . . . . . . . . . . . . . . 3 29.2.2 Parameters . . . . . . . . . . . . . . . . . . . . . . . . . 4 29.2.3 Proofs and end of proof . . . . . . . . . . . . . . . . . . 4 29.2.4 Examples (continued) . . . . . . . . . . . . . . . . . . . 4 29.3 Problem section . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 29.4 Numberings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 29.5 Fonts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 29.6 Maths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 29.7 Lists . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 29.8 Figures . . . . . . . . . . . . . . . . . . . . . .
On the Lattice of Prefix Codes
, 2000
"... The natural correspondence between prefix codes and trees is explored, generalizing the results obtained in [6] for the lattice of finite trees under division and the lattice of finite maximal prefix codes. Joins and meets of prefix codes are studied in this light in connection with such concepts as ..."
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The natural correspondence between prefix codes and trees is explored, generalizing the results obtained in [6] for the lattice of finite trees under division and the lattice of finite maximal prefix codes. Joins and meets of prefix codes are studied in this light in connection with such concepts as finiteness, maximality and varieties of rational languages. Decidability results are obtained for several problems involving rational prefix codes, including a partial solution to the primeness problem.