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Embedding of Systems of Affine Recurrence Equations in Coq
 in « Proc. TPHOLs 2003, 16th International Conference on Theorem Proving in Higher Order Logics », series LNCS
, 2003
"... Systems of affine recurrence equations (SAREs) over polyhedral domains are widely used to model computationintensive algorithms and to derive parallel code or hardware implementations. The development of complex SAREs for realsized applications calls for the elaboration of formal verification ..."
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Cited by 3 (1 self)
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Systems of affine recurrence equations (SAREs) over polyhedral domains are widely used to model computationintensive algorithms and to derive parallel code or hardware implementations. The development of complex SAREs for realsized applications calls for the elaboration of formal verification
Guaranteed minimumrank solutions of linear matrix equations via nuclear norm minimization
, 2007
"... The affine rank minimization problem consists of finding a matrix of minimum rank that satisfies a given system of linear equality constraints. Such problems have appeared in the literature of a diverse set of fields including system identification and control, Euclidean embedding, and collaborative ..."
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Cited by 551 (20 self)
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The affine rank minimization problem consists of finding a matrix of minimum rank that satisfies a given system of linear equality constraints. Such problems have appeared in the literature of a diverse set of fields including system identification and control, Euclidean embedding
Some efficient solutions to the affine scheduling problem  Part I Onedimensional Time
, 1996
"... Programs and systems of recurrence equations may be represented as sets of actions which are to be executed subject to precedence constraints. In many cases, actions may be labelled by integral vectors in some iteration domain, and precedence constraints may be described by affine relations. A s ..."
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Cited by 264 (22 self)
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Programs and systems of recurrence equations may be represented as sets of actions which are to be executed subject to precedence constraints. In many cases, actions may be labelled by integral vectors in some iteration domain, and precedence constraints may be described by affine relations. A
Converting affine recurrence equations to quasiuniform recurrence equations
 In AWOC 1988: Third International Workshop on Parallel Computation and VLSI Theory
, 1988
"... Most work on the problem of synthesizing a systolic array from a system of recurrence equations is restricted to systems of uniform recurrence equations. Recently, researchers have begun to relax this restriction to include systems of affine recurrence equations. A system of uniform recurrence equat ..."
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Cited by 8 (2 self)
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equations typically can be embedded in spacetime so that the distance between a variable and a dependent variable does not depend on the problem size. Systems of affine recurrence equations that are not uniform do not enjoy this property. A method is presented for converting a system of affine recurrence
The Coq Development Team
, 2007
"... c○INRIA 19992004 (COQ versions 7.x) c○INRIA 20042006 (COQ versions 8.x) This material may be distributed only subject to the terms and conditions set forth in the Open Publication License, v1.0 or later (the latest version is presently available at ..."
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c○INRIA 19992004 (COQ versions 7.x) c○INRIA 20042006 (COQ versions 8.x) This material may be distributed only subject to the terms and conditions set forth in the Open Publication License, v1.0 or later (the latest version is presently available at
Coinduction in Coq
 Lecture Notes of TYPES Summer School 2005, Sweden, Volume II
, 2005
"... When providing a collection of constructors to define an inductive type, we actually also define a dual operation: a destructor. This destructor is always defined using the same structure of patternmatching, so that we have a tendency to forget that we do extend the “patternmatching ” capability w ..."
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Cited by 4 (0 self)
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When providing a collection of constructors to define an inductive type, we actually also define a dual operation: a destructor. This destructor is always defined using the same structure of patternmatching, so that we have a tendency to forget that we do extend the “patternmatching ” capability with a new destructor at each definition. Constructors and destructors play a dual role in the definition of inductive types. Constructors produce elements of the inductive type, destructors consume elements of the inductive type. The inductive type itself is defined as the smallest collection of elements that is stable with respect to the constructors: it must contain all constants that are declared to be in the inductive type and all results of the constructors when the arguments of these constructors are already found to be in the inductive type. When considering structural recursion, recursive definitions are functions that consume elements of the inductive type. The discipline of structural recursion imposes that recursive calls consume data that is obtained through the destructor. The inductive type uses the constructors and destructors in a specific way. Coinductive
Proof Tactics for the Verification of Structured Systems of Affine Recurrence Equations
, 2003
"... Systems of affine recurrence equations (SAREs) over polyhedral domains are widely used to model computationintensive algorithms and to derive parallel code or hardware implementations. The development of complex SAREs for realsized applications calls for the elaboration of formal verification tech ..."
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Cited by 1 (0 self)
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Systems of affine recurrence equations (SAREs) over polyhedral domains are widely used to model computationintensive algorithms and to derive parallel code or hardware implementations. The development of complex SAREs for realsized applications calls for the elaboration of formal verification
Proof by Computation in the Coq system
 in Theoretical Computer Science
, 2000
"... In informal mathematics, statements involving computations are seldom proved. Instead, it is assumed that readers of the proof can carry out the computations on their own. However, when using an automated proof development system based on type theory, the user is forced to nd proofs for all claimed ..."
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Cited by 4 (2 self)
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In informal mathematics, statements involving computations are seldom proved. Instead, it is assumed that readers of the proof can carry out the computations on their own. However, when using an automated proof development system based on type theory, the user is forced to nd proofs for all claimed
The Naive Execution of Affine Recurrence Equations
 INTERNATIONAL CONFERENCE ON APPLICATIONSPECIFIC ARRAY PROCESSORS
, 1995
"... In recognition of the fundamental relation between regular arrays and systems of affine recurrence equations, the Alpha language was developed as the basis of a computer aided design methodology for regular array architectures. Alpha is used to initially specify algorithms at a very high algorith ..."
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Cited by 7 (4 self)
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In recognition of the fundamental relation between regular arrays and systems of affine recurrence equations, the Alpha language was developed as the basis of a computer aided design methodology for regular array architectures. Alpha is used to initially specify algorithms at a very high
Results 1  10
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98,598