Verification of sequential and concurrent programs
Verification of sequential and concurrent programs
An improved systolic algorithm for the algebraic path problem
Integration, the VLSI Journal - Special issue on algorithms and architectures
The Organization of Computations for Uniform Recurrence Equations
Journal of the ACM (JACM)
An axiomatic basis for computer programming
Communications of the ACM
DG2VHDL: A Tool to Facilitate the High Level Synthesisof Parallel Processing Array Architectures
Journal of VLSI Signal Processing Systems - Special issue on recent advances in the design and implementation of signal processing systems
Proving Properties of Multidimensional Recurrences with Application to Regular Parallel Algorithms
IPDPS '01 Proceedings of the 15th International Parallel & Distributed Processing Symposium
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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 well-suited to prove partial properties, equivalence properties between Alpha programs and properties that we cannot express within the Alpha language.