Results 1  10
of
13
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 ..."
Abstract

Cited by 3 (3 self)
 Add to MetaCart
(Show Context)
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.
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 ..."
Abstract

Cited by 3 (2 self)
 Add to MetaCart
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 ..."
Abstract

Cited by 2 (2 self)
 Add to MetaCart
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 for Trees
 Proceedings of the &quot;8th International Conference Automata and Formal Languages&quot;, 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. ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
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.
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 ..."
Abstract
 Add to MetaCart
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