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Tree Algebras
"... Many important families of regular languages have effective characterizations in terms of syntactic monoids or syntactic semigroups (see e.g. [1]). Definition of the syntactic monoid (resp. syntactic semigroup) of a language L ⊆ X ∗ (resp. a language L ⊆ X +) over an alphabet X requires regarding L ..."
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L as a subset of the free monoid X ∗ (resp. free semigroup X +). On the other hand tree languages have traditionally been regarded as subsets of term algebras. So it appears natural to base the classification of regular tree languages over a ranked alphabet Σ on their syntactic algebras as was done
TAX: A Tree Algebra for XML
 In Proc. DBPL Conf
, 2001
"... Querying XML has been the subject of much recent investigation. A formal bulk algebra is essential for applying databasestyle optimization to XML queries. We develop such an algebra, called TAX (Tree Algebra for XML), for manipulating XML data, modeled as forests of labeled ordered trees. Motivated ..."
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Cited by 122 (14 self)
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Querying XML has been the subject of much recent investigation. A formal bulk algebra is essential for applying databasestyle optimization to XML queries. We develop such an algebra, called TAX (Tree Algebra for XML), for manipulating XML data, modeled as forests of labeled ordered trees
Derivedtame Tree Algebras
"... In this note we classify the derivedtame tree algebras up to derived equivalence. A tree algebra is a basic algebra A = kQ/I whose quiver Q is a tree. The algebra A is said to be derivedtame when the repetitive category A of A is tame. We show that the tree algebra A is derivedtame precisely wh ..."
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Cited by 4 (0 self)
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In this note we classify the derivedtame tree algebras up to derived equivalence. A tree algebra is a basic algebra A = kQ/I whose quiver Q is a tree. The algebra A is said to be derivedtame when the repetitive category A of A is tame. We show that the tree algebra A is derivedtame precisely
GRADED BRAUER TREE ALGEBRAS
, 810
"... Abstract. In this paper we construct nonnegative gradings on a basic Brauer tree algebra AΓ corresponding to an arbitrary Brauer tree Γ of type (m, e). We do this by transferring gradings via derived equivalence from a basic Brauer tree algebra AS, whose tree is a star with the exceptional vertex i ..."
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Cited by 1 (1 self)
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Abstract. In this paper we construct nonnegative gradings on a basic Brauer tree algebra AΓ corresponding to an arbitrary Brauer tree Γ of type (m, e). We do this by transferring gradings via derived equivalence from a basic Brauer tree algebra AS, whose tree is a star with the exceptional vertex
The Ptree Algebra
, 2002
"... The Peano Count Tree (Ptree) is a quadrantbased lossless tree representation of the original spatial data. The idea of Ptree is to recursively divide the entire spatial data, such as Remotely Sensed Imagery data, into quadrants and record the count of 1bits for each quadrant, thus forming a quad ..."
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Cited by 23 (11 self)
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quadrant count tree. Using Ptree structure, all the count information can be calculated quickly. This facilitates efficient ways for data mining. In this paper, we will focus on the algebra and properties of Ptree structure and its variations. We have implemented fast algorithms for Ptree generation
Unranked Tree Algebra
, 2005
"... If in a transformation semigroup we assume that the set being acted upon has a semigroup structure, then the transformation semigroup can be used to recognize languages of unranked trees. This observation allows us to examine the relationship connecting languages of unranked trees with standard alge ..."
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Cited by 2 (0 self)
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If in a transformation semigroup we assume that the set being acted upon has a semigroup structure, then the transformation semigroup can be used to recognize languages of unranked trees. This observation allows us to examine the relationship connecting languages of unranked trees with standard
Homological Algebra of Mirror Symmetry
 in Proceedings of the International Congress of Mathematicians
, 1994
"... Mirror Symmetry was discovered several years ago in string theory as a duality between families of 3dimensional CalabiYau manifolds (more precisely, complex algebraic manifolds possessing holomorphic volume elements without zeroes). The name comes from the symmetry among Hodge numbers. For dual Ca ..."
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Cited by 529 (3 self)
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Mirror Symmetry was discovered several years ago in string theory as a duality between families of 3dimensional CalabiYau manifolds (more precisely, complex algebraic manifolds possessing holomorphic volume elements without zeroes). The name comes from the symmetry among Hodge numbers. For dual
Higher Dimensional Trees, Algebraically
"... Abstract. In formal language theory, James Rogers published a series of innovative papers generalising strings and trees to higher dimensions.Motivated by applications in linguistics, his goal was to smoothly extend the core theory of the formal languages of strings and trees to these higher dimensi ..."
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dimensions. Rogers ’ definitions focussed on a specific representation of higher dimensional trees. This paper presents an alternative approach which focusses more on their universal properties and is based upon category theory, algebras, coalgebras and containers. Our approach reveals that Rogers ’ trees
Tree algebras, semidiscreteness, and dilation theory
 Proc. London Math. Soc.(3) 68
, 1994
"... We introduce a class of finitedimensional algebras built from a partial order generated as a transitive relation from a finite tree. These algebras, known as tree algebras, have the property that every locally contractive representation has a *dilation. Furthermore, they satisfy an appropriate ana ..."
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Cited by 5 (4 self)
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We introduce a class of finitedimensional algebras built from a partial order generated as a transitive relation from a finite tree. These algebras, known as tree algebras, have the property that every locally contractive representation has a *dilation. Furthermore, they satisfy an appropriate
Results 1  10
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