Stephen F. Siegel

Using model checking with symbolic execution to verify parallel numerical programs

We present a method to verify the correctness of parallel programs that perform complex numerical computations, including computations involving floating-point arithmetic. The method requires that a sequential version of the program be provided, to serve as the specification for the parallel one. The key idea is to use model checking, together with symbolic execution, to establish the equivalence of the two programs.

THE HOCHSCHILD COHOMOLOGY RING OF A GROUP ALGEBRA

There is a standard additive decomposition of the Hochschild cohomology ring of the group algebra of a finite group

Model checking nonblocking MPI programs

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Combining symbolic execution with model checking to verify parallel numerical programs

as the direct sum of the cohomology rings of the centralizers of representatives of the conjugacy classes of

Formal analysis of MPI-based parallel programs

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Verification of MPI-Based Software for Scientific Computation

. A special case of our main result describes the cup product in terms of this decomposition. As applications, we determine presentations for the Hochschild cohomology rings of [(1)] the mod-

Modeling wildcard-free MPI programs for verification

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Verifying Parallel Programs with MPI-Spin

group algebra of the symmetric group

Automatic formal verification of MPI-based parallel programs

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TASS: The Toolkit for Accurate Scientific Software

, [(2)] the mod-