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320,372
On Kleene Algebras and Closed Semirings
, 1990
"... Kleene algebras are an important class of algebraic structures that arise in diverse areas of computer science: program logic and semantics, relational algebra, automata theory, and the design and analysis of algorithms. The literature contains several inequivalent definitions of Kleene algebras and ..."
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Cited by 55 (6 self)
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] and Salgebras [2] are strongly related by adjunctions. The axioms of Kleene algebra in the sense of [6] are not complete for the universal Horn theory of the regular events. This refutes a conjecture of Conway [2, p. 103]. Righthanded Kleene algebras are not necessarily lefthanded Kleene algebras
D.: Secondorder abstract interpretation via Kleene algebra
, 2004
"... Most standard approaches to the static analysis of programs, such as the popular worklist method, are firstorder values. In this paper we introduce a secondorder approach based on Kleene algebra. In this approach, the primary objects of interest are not the abstract data values, but the transfer f ..."
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Cited by 4 (1 self)
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functions that manipulate them. These elements form a lefthanded Kleene algebra. The dataflow labeling values, but rather by computing the star (Kleene closure) of a matrix of transfer functions. In this paper we introduce the method and prove soundness and completeness with respect to the standard
Bytecode 2005 Preliminary Version Kleene Algebra and Bytecode Verification Abstract
"... Most standard approaches to the static analysis of programs, such as the popular worklist method, are firstorder methods that inductively annotate program points with abstract values. In [6] we introduced a secondorder approach based on Kleene algebra. In this approach, the primary objects of inte ..."
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of interest are not the abstract data values, but the transfer functions that manipulate them. These elements form a lefthanded Kleene algebra. The dataflow labeling is not achieved by inductively labeling the program with abstract values, but rather by computing the star (Kleene closure) of a matrix
LeftHanded Completeness
, 2011
"... We give a new, significantly shorter proof of the completeness of the lefthanded star rule of Kleene algebra. The proof reveals the rich interaction of algebra and coalgebra in the theory. 1 ..."
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Cited by 1 (0 self)
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We give a new, significantly shorter proof of the completeness of the lefthanded star rule of Kleene algebra. The proof reveals the rich interaction of algebra and coalgebra in the theory. 1
Kleene algebra with tests
 Transactions on Programming Languages and Systems
, 1997
"... Abstract. We investigate conditions under which a given Kleene algebra with tests is isomorphic to an algebra of binary relations. Two simple separation properties are identified that, along with starcontinuity, are sufficient for nonstandard relational representation. An algebraic condition is ide ..."
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Cited by 153 (29 self)
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Abstract. We investigate conditions under which a given Kleene algebra with tests is isomorphic to an algebra of binary relations. Two simple separation properties are identified that, along with starcontinuity, are sufficient for nonstandard relational representation. An algebraic condition
An Extended Set of Fortran Basic Linear Algebra Subprograms
 ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE
, 1986
"... This paper describes an extension to the set of Basic Linear Algebra Subprograms. The extensions are targeted at matrixvector operations which should provide for efficient and portable implementations of algorithms for high performance computers. ..."
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Cited by 526 (72 self)
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This paper describes an extension to the set of Basic Linear Algebra Subprograms. The extensions are targeted at matrixvector operations which should provide for efficient and portable implementations of algorithms for high performance computers.
A completeness theorem for Kleene algebras and the algebra of regular events
 Information and Computation
, 1994
"... We givea nitary axiomatization of the algebra of regular events involving only equations and equational implications. Unlike Salomaa's axiomatizations, the axiomatization given here is sound for all interpretations over Kleene algebras. 1 ..."
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Cited by 250 (28 self)
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We givea nitary axiomatization of the algebra of regular events involving only equations and equational implications. Unlike Salomaa's axiomatizations, the axiomatization given here is sound for all interpretations over Kleene algebras. 1
A Compositional Approach to Performance Modelling
, 1996
"... Performance modelling is concerned with the capture and analysis of the dynamic behaviour of computer and communication systems. The size and complexity of many modern systems result in large, complex models. A compositional approach decomposes the system into subsystems that are smaller and more ea ..."
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Cited by 746 (102 self)
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easily modelled. In this thesis a novel compositional approach to performance modelling is presented. This approach is based on a suitably enhanced process algebra, PEPA (Performance Evaluation Process Algebra). The compositional nature of the language provides benefits for model solution as well
Comprehending Monads
 Mathematical Structures in Computer Science
, 1992
"... Category theorists invented monads in the 1960's to concisely express certain aspects of universal algebra. Functional programmers invented list comprehensions in the 1970's to concisely express certain programs involving lists. This paper shows how list comprehensions may be generalised t ..."
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Cited by 522 (16 self)
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Category theorists invented monads in the 1960's to concisely express certain aspects of universal algebra. Functional programmers invented list comprehensions in the 1970's to concisely express certain programs involving lists. This paper shows how list comprehensions may be generalised
LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares
 ACM Trans. Math. Software
, 1982
"... An iterative method is given for solving Ax ~ffi b and minU Ax b 112, where the matrix A is large and sparse. The method is based on the bidiagonalization procedure of Golub and Kahan. It is analytically equivalent to the standard method of conjugate gradients, but possesses more favorable numerica ..."
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Cited by 649 (21 self)
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gradient algorithms, indicating that I~QR is the most reliable algorithm when A is illconditioned. Categories and Subject Descriptors: G.1.2 [Numerical Analysis]: ApprorJmationleast squares approximation; G.1.3 [Numerical Analysis]: Numerical Linear Algebralinear systems (direct and
Results 1  10
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320,372