In this paper we unify the two subjects of implicitization and parametrization of nonsingular cubic surfaces. Beginning with a cubic parametrization with six basepoints, we first form a three by four Hilbert–Burch matrix, and then a three by three matrix of linear forms whose determinant is the implicit equation. Beginning with an implicit equation, we show how to construct a three by three mat...

Much automatic pipeline verification research of the last decade has been based on some form of “Burch-Dill flushing” [BD94]. In this work, we study synchronization-at-retirement, an alternative formulation of correctness for pipelines. In this formulation, the proof obligations can also be verified automatically but have significantly-reduced verification complexity compared to flushing. We pr...

Bongani M Mayosi ([email protected]) Charles Shey Wiysonge ([email protected]) Mpiko Ntsekhe ([email protected]) Jimmy A Volmink ([email protected]) Freedom Gumedze ([email protected]) Gary Maartens ([email protected]) Akinyemi Aje ([email protected]) Baby M Thomas ([email protected]) Kandathil M Thomas ([email protected]) Abolade A Aw...

Let  be a local Cohen-Macaulay ring with infinite residue field,  an Cohen - Macaulay module and  an ideal of  Consider  and , respectively, the Rees Algebra and associated graded ring of , and denote by  the analytic spread of  Burch’s inequality says that  and equality holds if  is Cohen-Macaulay. Thus, in that case one can compute the depth of associated graded ring of  as  In this paper we ...

This paper extends Burch and Dill’s pipeline verification method [4] to the bit level. We introduce the idea of memory shadowing, a new technique for providing on-the-fly identical initial memory state to two different memory execution sequences. We also present an algorithm which compares the final states of two memories for equality. Memory shadowing and the comparison algorithm build on the ...