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103
Axiomatising Divergence
, 2002
"... This paper develops sound and complete axiomatisations for the divergence sensitive spectrum of weak bisimulation equivalence. The axiomatisations can be extended to a considerable fragment of the linear time  branching time spectrum with silent moves, partially solving an open problem posed in [5 ..."
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This paper develops sound and complete axiomatisations for the divergence sensitive spectrum of weak bisimulation equivalence. The axiomatisations can be extended to a considerable fragment of the linear time  branching time spectrum with silent moves, partially solving an open problem posed
Kleene Monads: Handling Iteration in a Framework of Generic Effects
"... Abstract. Monads are a wellestablished tool for modelling various computational effects. They form the semantic basis of Moggi’s computational metalanguage, the metalanguage of effects for short, which made its way into modern functional programming in the shape of Haskell’s donotation. Standard c ..."
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Cited by 4 (2 self)
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metalanguage of control and effects over continuous Kleene monads fails to be recursively enumerable. We proceed to identify a fragment of this language which still contains both Kleene algebra and the metalanguage of effects and for which the natural axiomatisation is complete, and indeed the equational
A Singular Loop Transformation Framework Based on Nonsingular Matrices
, 1992
"... In this paper, we discuss a loop transformation framework that is based on integer nonsingular matrices. The transformations included in this framework are called transformations and include permutation, skewing and reversal, as well as a transformation called loop scaling. This framework is mo ..."
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Cited by 130 (8 self)
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is more general than existing ones; however, it is also more difficult to generate code in our framework. This paper shows how integer lattice theory can be used to generate efficient code. An added advantage of our framework over existing ones is that there is a simple completion algorithm which
Completions, reversals, and duality for tropical varieties
"... Abstract. The algebraic foundation of tropical polynomial algebra provides the framework for the geometric construction of the supplement and the reversal of tropical varieties, thereby inducing a duality of reduced tropical varieties; for classes of tropical hypersurfaces the corresponding point sy ..."
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Cited by 4 (2 self)
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Abstract. The algebraic foundation of tropical polynomial algebra provides the framework for the geometric construction of the supplement and the reversal of tropical varieties, thereby inducing a duality of reduced tropical varieties; for classes of tropical hypersurfaces the corresponding point
IDEAL LATTICES OF LATTICES
, 1975
"... This paper shows that any compactly generated lattice is a subdirect product of subdirectly irreducible lattices which are complete and upper continuous. An example of a compactly generated lattice which cannot be subdirectly decomposed into subdirectly irreducible compactly generated lattices is gi ..."
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This paper shows that any compactly generated lattice is a subdirect product of subdirectly irreducible lattices which are complete and upper continuous. An example of a compactly generated lattice which cannot be subdirectly decomposed into subdirectly irreducible compactly generated lattices
Macneille completions and canonical extensions
 Transactions of the American Mathematical Society
"... Abstract. Let V be a variety of monotone bounded lattice expansions, that is, bounded lattices endowed with additional operations, each of which is order preserving or reversing in each coordinate. We prove that if V is closed under MacNeille completions, then it is also closed under canonical exten ..."
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Cited by 21 (8 self)
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Abstract. Let V be a variety of monotone bounded lattice expansions, that is, bounded lattices endowed with additional operations, each of which is order preserving or reversing in each coordinate. We prove that if V is closed under MacNeille completions, then it is also closed under canonical
The theory of ulattices
"... The concept of a ualgebra for an equational theory T = h\Omega, Ei was introducedin [10]. If the underlying set of a Talgebra is a complete lattice and if the operations from \Omega preserve the partial order, the existence of least and greatestfixpoints makes it possible to interpret uterms, wh ..."
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The concept of a ualgebra for an equational theory T = h\Omega, Ei was introducedin [10]. If the underlying set of a Talgebra is a complete lattice and if the operations from \Omega preserve the partial order, the existence of least and greatestfixpoints makes it possible to interpret u
On the lattice of subpseudovarieties of DA
"... Abstract. The wealth of information that is available on the lattice of varieties of bands, is used to illuminate the structure of the lattice of subpseudovarieties of DA, a natural generalization of bands which plays an important role in language theory and in logic. The main result describes a hi ..."
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Cited by 6 (6 self)
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hierarchy of decidable subpseudovarieties of DA in terms of iterated Mal’cev products with the pseudovarieties of definite and reverse definite semigroups. The complete elucidation of the structure of the lattice LB of band varieties is one of the jewels of semigroup theory: this lattice turns out
Basic Process Algebra with Iteration: Completeness of its Equational Axioms
 Computer Journal
, 1993
"... Bergstra, Bethke & Ponse [BBP93] proposed an axiomatisation for Basic Process Algebra extended with iteration. In this paper, we prove that this axiomatisation is complete with respect to bisimulation equivalence. To obtain this result, we will set up a term rewriting system, based on the axioms ..."
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Bergstra, Bethke & Ponse [BBP93] proposed an axiomatisation for Basic Process Algebra extended with iteration. In this paper, we prove that this axiomatisation is complete with respect to bisimulation equivalence. To obtain this result, we will set up a term rewriting system, based
On the completeness and decidability of Duration Calculus with iteration. Theoretical Computer Science
, 2005
"... The extension of the Duration Calculus (DC) by iteration, which is also known as Kleene star, enables the straightforward specification of repetitive behaviour in DC and facilitates the translation of design descriptions between DC, timed regular expressions and timed automata. In this paper we pre ..."
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Cited by 11 (7 self)
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and rule in various ways in order to axiomatise iteration completely. The additions we propose include either the proof rule or an induction axiom. We also present results on the decidability of a subset of the extension DC ∗ of DC by iteration.
Results 1  10
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103