Sequential Real Number Computation and Recursive Relations

Relations Among Parallel and Sequential Computation Models

This paper relates uniform small-depth circuit families as a parallel computation model with the complexity of polynomial time Turing machines. Among the consequences we obtain are: (a) a collapse of two circuit classes is equivalent to a relativizable collapse of the two corresponding polynomial time classes; and (b) a collapse of uniformity conditions for small depth circuits is equivalent to...

Time-recursive computation and real-time parallel architectures: a framework

The time-recursive computation has been proven a particularly useful tool in real-time data compression, in transform domain adaptive filtering, and in spectrum analysis. Unlike the FFT-based ones, the time-recursive architectures require only local communication. Also, they are modular and regular, thus they are very appropriate for VLSI implementation and they allow a high degree of paralleli...

On the non-sequential nature of the interval-domain model of real-number computation

We show that real-number computations in the interval-domain environment are “inherently parallel” in a precise mathematical sense. We do this by reducing computations of the weak parallel-or operation on the Sierpinski domain to computations of the addition operation on the interval domain.

Real number computation through Gray code embedding

Well-Founded Recursive Relations

We give a short constructive proof of the fact that certain binary relations > are well-founded, given a lifting à la Ferreira-Zantema and a wellfounded relation .. This construction generalizes several variants of the recursive path ordering on terms and of the Knuth-Bendix ordering. It also applies to other domains, of graphs, of infinite terms, of word and tree automata notably. We then exte...