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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 ..."
Abstract

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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 . . .
, 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.