## Proving properties of multidimensional recurrences with application to regular parallel algorithms (2001)

Venue: | In FMPPTA’01 |

Citations: | 2 - 1 self |

### BibTeX

@INPROCEEDINGS{Cachera01provingproperties,

author = {D. Cachera and P. Quinton and S. Rajopadhye and T. Risset},

title = {Proving properties of multidimensional recurrences with application to regular parallel algorithms},

booktitle = {In FMPPTA’01},

year = {2001},

pages = {1491--1498}

}

### OpenURL

### Abstract

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 M-MAlpha environment using the PVS theorem prover. 1

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Citation Context ... an extension of the formalism of recurrence equations, specifically that of Systems of Affine Recurrence Equations (SAREs) over polyhedral domains. TheALPHA language [18] and the MMALPHA environment =-=[17]-=- provide the syntax and tools to handle such recurrence equations. The MMALPHA environment implements polyhedral transformations that allow us to start from a high level specification and refine it to... |

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Citation Context ...We present here a set of proof methods that can be used to formally verify properties of SAREs. Many embeddings of languages in logical frameworks like HOL, Coq, PVS, etc. have been investigated (see =-=[12, 2, 5]-=- for instance). The originality of our approach is that it combines semanticspreserving polyhedral transformations with calls to a theorem prover. On one hand, the polyhedral model provides powerful t... |

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Citation Context ...ethods. The polyhedral model uses an extension of the formalism of recurrence equations, specifically that of Systems of Affine Recurrence Equations (SAREs) over polyhedral domains. TheALPHA language =-=[18]-=- and the MMALPHA environment [17] provide the syntax and tools to handle such recurrence equations. The MMALPHA environment implements polyhedral transformations that allow us to start from a high lev... |

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Citation Context ...We present here a set of proof methods that can be used to formally verify properties of SAREs. Many embeddings of languages in logical frameworks like HOL, Coq, PVS, etc. have been investigated (see =-=[12, 2, 5]-=- for instance). The originality of our approach is that it combines semanticspreserving polyhedral transformations with calls to a theorem prover. On one hand, the polyhedral model provides powerful t... |

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Citation Context ...We present here a set of proof methods that can be used to formally verify properties of SAREs. Many embeddings of languages in logical frameworks like HOL, Coq, PVS, etc. have been investigated (see =-=[12, 2, 5]-=- for instance). The originality of our approach is that it combines semanticspreserving polyhedral transformations with calls to a theorem prover. On one hand, the polyhedral model provides powerful t... |

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Citation Context ... evolves from undefined into valued, and does not change once it has been given a value. Operational semantics have been defined as a preamble to the definition of invariant-based proof methodologies =-=[3]-=-. Practically interesting ALPHA programs belong to a class called schedulable systems, i.e., systems for which we are able to define an execution order on computations (a timing function) compatible w... |

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Citation Context ...igure 3. Checking a non linear timing functionsA non linear schedule A large variety of algorithms can be derived from the initial system, e.g. by pipelining variables or modifying the domain’s shape =-=[6, 13]-=-. For one of these versions, a particular timing function has been discovered. As it has not been given by an automatic scheduling algorithm, we want to check that this function, namely t[i� j� k� N ]... |

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Citation Context ...f equations, or when we want to prove a property that is not expressible in the formalism of affine recurrence equations. More generally, the development of more complex and structured ALPHA programs =-=[7]-=- has called for the elaboration of verification methodologies. We present here a set of proof methods that can be used to formally verify properties of SAREs. Many embeddings of languages in logical f... |