Title

A mathematics of arrays

Date of Award

1988

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Electrical Engineering and Computer Science

Advisor(s)

Ernest Sibert

Keywords

Array expressions, Shapes

Subject Categories

Computer Sciences

Abstract

The ability to describe array expressions in terms of the shapes of their arguments and the symbolic verification of n-dimensional array expressions has been an open area of research in theoretical computer science. A class of operations which includes the inner and outer product of array expressions is defined using shapes. An indexing function $\Psi$ is the basis of all definitions, while a higher order operation $\Omega$ extends the operations to apply to any dimension. The theory presented is followed by an application to hardware design verification. Progress on the formal design, implementation, and verification of a basis for a parallel language with arrays including the scheduling of subarray operations (asynchronous events) to the processors of shared-memory MIMD architectures is discussed.

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