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A bialgebraic review of regular expressions, deterministic automata and languages
 Techn. Rep. ICISR05003, Inst. for Computing and Information Sciences, Radboud Univ
, 2005
"... To Joseph Goguen on the occasion of his 65th birthday1. Abstract. This papers reviews the classical theory of deterministic automata and regular languages from a categorical perspective. The basis is formed by Rutten’s description of the Brzozowski automaton structure in a coalgebraic framework. We ..."
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Cited by 3 (2 self)
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To Joseph Goguen on the occasion of his 65th birthday1. Abstract. This papers reviews the classical theory of deterministic automata and regular languages from a categorical perspective. The basis is formed by Rutten’s description of the Brzozowski automaton structure in a coalgebraic framework. We
Axioms for Weak Bialgebras
, 1998
"... Let (A; 1) be a finite dimensional unital associative algebra over a field K, which is also equipped with a coassociative counital coalgebra structure (\Delta; "). A is called a weak bialgebra if the coproduct \Delta : A ! A\Omega A satisfies \Delta(ab) = \Delta(a)\Delta(b). We do not require ..."
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Cited by 33 (2 self)
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Let (A; 1) be a finite dimensional unital associative algebra over a field K, which is also equipped with a coassociative counital coalgebra structure (\Delta; "). A is called a weak bialgebra if the coproduct \Delta : A ! A\Omega A satisfies \Delta(ab) = \Delta(a)\Delta(b). We do not require
BRAIDED LIE BIALGEBRAS
, 1997
"... We introduce braided Lie bialgebras as the infinitesimal version of braided groups. They are Lie algebras and Lie coalgebras with the coboundary of the Lie cobracket an infinitesimal braiding. We provide theorems of transmutation, Lie biproduct, bosonisation and doublebosonisation relating braided ..."
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Cited by 2 (0 self)
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We introduce braided Lie bialgebras as the infinitesimal version of braided groups. They are Lie algebras and Lie coalgebras with the coboundary of the Lie cobracket an infinitesimal braiding. We provide theorems of transmutation, Lie biproduct, bosonisation and doublebosonisation relating
AND LIE BIALGEBRA STRUCTURES
, 1995
"... Lie bialgebra structures on e(2) are classified. For two Lie bialgebra structures which are not coboundaries (i.e. which are not determined by a classical rmatrix) we solve the cocycle condition, find the LiePoisson brackets and obtain quantum group relations. There is one to one correspondence be ..."
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Lie bialgebra structures on e(2) are classified. For two Lie bialgebra structures which are not coboundaries (i.e. which are not determined by a classical rmatrix) we solve the cocycle condition, find the LiePoisson brackets and obtain quantum group relations. There is one to one correspondence
THERMAL FIELD DYNAMICS AND BIALGEBRAS
, 1996
"... Abstract. In Thermal Field Dynamics, thermal states are obtained from restrictions of vacuum states on a doubled field algebra. It is shown that the suitably doubled Fock representations of the Heisenberg algebra do not need to be introduced by hand but can be canonically handed down from deformatio ..."
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deformations of the extended Heisenberg bialgebra. No artificial redefinitions of fields are necessary to obtain the thermal representations and the case of arbitrary dimension is considered from the beginning. Our results support a possibly fundamental role of bialgebra structures in defining a general
Sorting with Bialgebras and Distributive Laws
"... Sorting algorithms are an intrinsic part of functional programming folklore as they exemplify algorithm design using folds and unfolds. This has given rise to an informal notion of duality among sorting algorithms: insertion sorts are dual to selection sorts. Using bialgebras and distributive laws, ..."
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Cited by 1 (1 self)
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Sorting algorithms are an intrinsic part of functional programming folklore as they exemplify algorithm design using folds and unfolds. This has given rise to an informal notion of duality among sorting algorithms: insertion sorts are dual to selection sorts. Using bialgebras and distributive laws
Results 1  10
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1,414