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Bisimulation for Probabilistic Transition Systems: A Coalgebraic Approach
, 1998
"... . The notion of bisimulation as proposed by Larsen and Skou for discrete probabilistic transition systems is shown to coincide with a coalgebraic definition in the sense of Aczel and Mendler in terms of a set functor. This coalgebraic formulation makes it possible to generalize the concepts to a ..."
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Cited by 105 (15 self)
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. The notion of bisimulation as proposed by Larsen and Skou for discrete probabilistic transition systems is shown to coincide with a coalgebraic definition in the sense of Aczel and Mendler in terms of a set functor. This coalgebraic formulation makes it possible to generalize the concepts
A Coalgebraic Approach to Kleene Algebra with Tests
 In volume 82(1) of ENTCS
, 2003
"... Kleene Algebra with Tests is an extension of Kleene Algebra, the algebra of regular expressions, which can be used to reason about programs. We develop a coalgebraic theory of Kleene Algebra with Tests, along the lines of the coalgebraic theory of regular expressions based on deterministic automata. ..."
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Cited by 9 (0 self)
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Kleene Algebra with Tests is an extension of Kleene Algebra, the algebra of regular expressions, which can be used to reason about programs. We develop a coalgebraic theory of Kleene Algebra with Tests, along the lines of the coalgebraic theory of regular expressions based on deterministic automata
A coalgebraic approach to the semantics of the ambient calculus
 ALGEBRA AND COALGEBRA IN COMPUTER SCIENCE
, 2005
"... Recently, various process calculi have been introduced which are suited for the modelling of mobile computation and in particular the mobility of program code; a prominent example is the ambient calculus. Due to the complexity of the involved spatial reduction, there is — in contrast to the situatio ..."
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Cited by 5 (2 self)
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to the situation in standard process algebra — up to now no satisfying coalgebraic representation of a mobile process calculus. Here, we discuss a coalgebraic denotational semantics for the ambient calculus, viewed as a step towards a generic coalgebraic framework for modelling mobile systems. Crucial features
An abstract coalgebraic approach to process equivalence for wellbehaved operational semantics
, 2004
"... This thesis is part of the programme aimed at finding a mathematical theory of wellbehaved structural operational semantics. General and basic results shown in 1997 in a seminal paper by Turi and Plotkin are extended in two directions, aiming at greater expressivity of the framework. The socalled ..."
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Cited by 23 (5 self)
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to cover other operational equivalences and preorders (e.g. trace equivalence), known collectively as the van Glabbeek spectrum. To do this, a novel coalgebraic approach to relations on processes is desirable, since the usual approach to coalgebraic bisimulations as spans of coalgebras does not extend
Domain Theory
 Handbook of Logic in Computer Science
, 1994
"... Least fixpoints as meanings of recursive definitions. ..."
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Cited by 546 (25 self)
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Least fixpoints as meanings of recursive definitions.
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 CalabiYau manifolds V, W of dimension n (not necessarily equal to 3) one has dim H p (V, Ω q) = dim H n−p (W, Ω q). Physicists conjectured that conformal field theories associated with mirror varieties are equivalent. Mathematically, MS is considered now as a relation between numbers of rational curves on such a manifold and Taylor coefficients of periods of Hodge structures considered as functions on the moduli space of complex structures on a mirror manifold. Recently it has been realized that one can make predictions for numbers of curves of positive genera and also on CalabiYau manifolds of arbitrary dimensions. We will not describe here the complicated history of the subject and will not mention many beautiful contsructions, examples and conjectures motivated
Coalgebraic Approach to the Loday Infinity Category, Stem Differential for 2nary Graded and Homotopy Algebras. Preprint Arxive
"... We define a graded twistedcoassociative coproduct on the tensor algebra TW of any Z ngraded vector space W. If W is the desuspension space ↓ V of a graded vector space V, the coderivations (resp. quadratic “degree 1 ” codifferentials, arbitrary odd codifferentials) of this coalgebra are 1to1 wit ..."
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Cited by 17 (6 self)
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We define a graded twistedcoassociative coproduct on the tensor algebra TW of any Z ngraded vector space W. If W is the desuspension space ↓ V of a graded vector space V, the coderivations (resp. quadratic “degree 1 ” codifferentials, arbitrary odd codifferentials) of this coalgebra are 1to1
A Tutorial on (Co)Algebras and (Co)Induction
 EATCS Bulletin
, 1997
"... . Algebraic structures which are generated by a collection of constructors like natural numbers (generated by a zero and a successor) or finite lists and trees are of wellestablished importance in computer science. Formally, they are initial algebras. Induction is used both as a definition pr ..."
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Cited by 269 (36 self)
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principle, and as a proof principle for such structures. But there are also important dual "coalgebraic" structures, which do not come equipped with constructor operations but with what are sometimes called "destructor" operations (also called observers, accessors, transition maps
Coalgebraic Logic
 Annals of Pure and Applied Logic
, 1999
"... We present a generalization of modal logic to logical systems which are interpreted on coalgebras of functors on sets. The leading idea is that infinitary modal logic contains characterizing formulas. That is, every modelworld pair is characterized up to bisimulation by an infinitary formula. The ..."
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Cited by 108 (0 self)
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We present a generalization of modal logic to logical systems which are interpreted on coalgebras of functors on sets. The leading idea is that infinitary modal logic contains characterizing formulas. That is, every modelworld pair is characterized up to bisimulation by an infinitary formula
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