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Validation of Mixed SignalAlpha RealTime Systems through Affine Calculus on Clock Synchronisation Constraints
 In World Congress on Formal Methods (2
, 1999
"... . In this paper we present the affine clock calculus as an extension of the formal verification techniques provided by the Signal language. A Signal program describes a system of clock synchronisation constraints the consistency of which is verified by compilation (clock calculus) . Welladapted ..."
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. In this paper we present the affine clock calculus as an extension of the formal verification techniques provided by the Signal language. A Signal program describes a system of clock synchronisation constraints the consistency of which is verified by compilation (clock calculus) . Welladapted in controlbased system design, the clock calculus has to be extended in order to enable the validation of SignalAlpha applications which usually contain important numerical calculations. The new affine clock calculus is based on the properties of affine relations induced between clocks by the refinement of SignalAlpha specifications in a codesign context. Affine relations enable the derivation of a new set of synchronisability rules which represent conditions against which synchronisation constraints on clocks can be assessed. Properties of affine relations and synchronisability rules are derived in the semantical model of traces of Signal. A prototype implementing a subset of t...
Structuration of the alpha language
 In Massively Parallel Programming Models
, 1995
"... This paper presents extensions to Alpha, a language based upon the formalism of affine recurrence equations (AREs). These extensions address the need for parametric and structured systems of such AREs. Similar to, but more general as the map operator of classical functional languages, the Alpha stru ..."
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This paper presents extensions to Alpha, a language based upon the formalism of affine recurrence equations (AREs). These extensions address the need for parametric and structured systems of such AREs. Similar to, but more general as the map operator of classical functional languages, the Alpha structuration techniques provide a dense and powerful description of complex systems referencing each other. Such structured systems of AREs may be interpreted as (or translated into) sequential function calls, hierarchical hardware description, or any SIMD flavour of structured programming. With the help of examples, we give an overview of these techniques, and their substitution semantics based on the homomorphic extension of convex polyedra and affine functions.
Verification of safety properties for parameterized regular systems
, 2005
"... We propose a combination of heuristic methods to prove properties of control signals for regular systems defined by means of affine recurrence equations (AREs). We benefit from the intrinsic regularity of the underlying polyhedral model to handle parameterized systems in a symbolic way. Our techniqu ..."
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We propose a combination of heuristic methods to prove properties of control signals for regular systems defined by means of affine recurrence equations (AREs). We benefit from the intrinsic regularity of the underlying polyhedral model to handle parameterized systems in a symbolic way. Our techniques apply to safety properties. The general proof process consists in an iteration that alternates two heuristics. We are able to identify the cases when this iteration will stop in a finite number of steps. These techniques have been implemented in a high level synthesis environment based on the polyhedral model.
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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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 techniques. As the systems we consider are generic, i.e., depend on parameters whose value are not statically known, we considered using theorem provers, and have implemented a translation from SAREs into the Coq system. We take advantage of the regularity of our model to automatically generate an inductive type adapted to each particular system. This allows us to automatically prove that the functional translation of equations respects the wanted fixpoint properties, and to systematically derive mutual induction schemes.
Proving properties of multidimensional recurrences with application to regular parallel algorithms
 In FMPPTA’01
, 2001
"... We present a set of verification methods to prove properties of parallel systems described by means of multidimensional affine recurrence equations. We use polyhedral analysis and transformation techniques together with theorem proving. Polyhedral techniques allow us to handle simple but otherwise c ..."
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We present a set of verification methods to prove properties of parallel systems described by means of multidimensional affine recurrence equations. We use polyhedral analysis and transformation techniques together with theorem proving. Polyhedral techniques allow us to handle simple but otherwise costly proof steps, while theorem proving provides more expressivity and more complex proof techniques. This allows large, generic and structured systems to be verified. These methods are implemented in the MMAlpha environment using the PVS theorem prover. 1
A logical framework to prove properties of ALPHA programs
, 1997
"... : We present an assertional approach to prove properties of Alpha programs. Alpha is a functional language based on affine recurrence equations. We first present two kinds of operational semantics for Alpha together with some equivalence and confluence properties of these semantics. We then present ..."
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: We present an assertional approach to prove properties of Alpha programs. Alpha is a functional language based on affine recurrence equations. We first present two kinds of operational semantics for Alpha together with some equivalence and confluence properties of these semantics. We then present an attempt to provide Alpha with an external logical framework. We therefore define a proof method based on invariants. We focus on a particular class of invariants, namely canonical invariants, that are a logical expression of the program's semantics. We finally show that this framework is wellsuited to prove partial properties, equivalence properties between Alpha programs and properties that we cannot express within the Alpha language. Keywords: Concurrent programming, recurrence equations, specifying and verifying and reasoning about programs, semantics of programming languages, dataparallel languages, proof methodology, invariants. (R'esum'e : tsvp) This work has been partly suppor...
Libraries of schedulefree operators in Alpha
 in: Proceedings of the International Conference on Application Speci®c Array Processors, IEEE Computer
, 1997
"... This paper presents a method, based on the formalism of affine recurrence equations, for the synthesis of digital circuits exploiting parallelism at the bitlevel. In the initial specification of a numerical algorithm, the arithmetic operators are replaced with their yet unscheduled (schedulefree) ..."
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This paper presents a method, based on the formalism of affine recurrence equations, for the synthesis of digital circuits exploiting parallelism at the bitlevel. In the initial specification of a numerical algorithm, the arithmetic operators are replaced with their yet unscheduled (schedulefree) binary implementation as recurrence equations. This allows a bitlevel dependency analysis yielding a bitparallel array. The method is demonstrated on the example of the matrixvector product, and discuted. 1
The ALPHA Compiler and Uncompiler
"... : The Alpha parser translates an Alpha source program into an abstract syntax tree (AST). The Alpha unparser, or pretty printer, does the opposite translation from an Alpha AST back to a source program. These two translators are an integral part of the Alpha environment. This report is both a user's ..."
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: The Alpha parser translates an Alpha source program into an abstract syntax tree (AST). The Alpha unparser, or pretty printer, does the opposite translation from an Alpha AST back to a source program. These two translators are an integral part of the Alpha environment. This report is both a user's guide and techical documentation for these two programs. Keywords: recurrence equations, systolic arrays, hardward design language (R'esum'e : tsvp) email: wilde@irisa.frThiswork was partially supported by the Esprit Basic Research Action NANA 2, Number 6632 and by NSF Grant No. MIP910852. Centre National de la Recherche Scientifique Institut National de Recherche en Informatique (URA 227) Universit e de Rennes 1  Insa de Rennes et en Automatique  unit e de recherche de Rennes Le compilateur et d'ecompilateur de ALPHA Rapport Technique R'esum'e : Le compilateur d'Alpha traduit un programme 'ecrit en Alpha vers un arbre de syntaxe abstract (AST). Le d'ecompilateur d'Alpha fait l'...
Automatic Synthesis of Regular Architectures Optimized at the Bit Level
, 1997
"... : This paper presents methods based on the formalism of affine recurrence equations for the synthesis of bitlevel regular architectures from wordlevel (integer or real) algorithms. Because of bitlevel dependency analysis, the arrays have optimal efficiency. We present two possible design flows le ..."
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: This paper presents methods based on the formalism of affine recurrence equations for the synthesis of bitlevel regular architectures from wordlevel (integer or real) algorithms. Because of bitlevel dependency analysis, the arrays have optimal efficiency. We present two possible design flows leading to architectures based either on bitparallel or bitserial operators. The first one is fully automated. Keywords: high level synthesis, regular arrays, arithmetic operators (R'esum'e : tsvp) Also published in the Proceedings of the Workshop on Design Methodologies for Signal Processing  Zakopane, Poland  2930 August 1996 * This research is partly supported by CNET/France Telecom. ** ffdupontg,flemoenneg@irisa.fr CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE Centre National de la Recherche Scientifique Institut National de Recherche en Informatique (URA 227) Universit e de Rennes 1  Insa de Rennes et en Automatique  unit e de recherche de Rennes Synth`ese automatique...
A logical framework to prove . . .
, 1997
"... We present an assertional approach to prove properties of Alpha programs. Alpha is a functional language based on affine recurrence equations. We first present two kinds of operational semantics for Alpha together with some equivalence and confluence properties of these semantics. We then present ..."
Abstract
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We present an assertional approach to prove properties of Alpha programs. Alpha is a functional language based on affine recurrence equations. We first present two kinds of operational semantics for Alpha together with some equivalence and confluence properties of these semantics. We then present an attempt to provide Alpha with an external logical framework. We therefore define a proof method based on invariants. We focus on a particular class of invariants, namely canonical invariants, that are a logical expression of the program's semantics. We finally show that this framework is wellsuited to prove partial properties, equivalence properties between Alpha programs and properties that we cannot express within the Alpha language.