Regular frequency computations

Regular frequency computations

An (m,n)-computation of a function f is given by a deterministic Turing machine which on n pairwise different inputs produces n output values where at least m of the n values are in accordance with f . In such a case we say that the Turing machine computes f with frequency ≥ m/n. The most prominent result for frequency computations is due to Trakhtenbrot: The class of (m,n)-computable functions...

A structural property of regular frequency computations

GCD Computations Modulo Regular Chains

The computation of triangular decompositions involves two fundamental operations: polynomial GCDs modulo regular chains and regularity test modulo saturated ideals. We propose new algorithms for these core operations based on modular methods and fast polynomial arithmetic. We rely on new results connecting polynomial subresultants and GCDs modulo regular chains. We report on extensive experimen...

Time Bounded Frequency Computations

This disproves a conjecture of Kinber. (2) We give a transparent proof of a generalization of Kinber's result that there exist arbitrarily complex problems admitting a polynomial time frequency computation. Several corollaries provide more insight into the structure of the hierarchy of polynomial time frequency classes. (3) The relationships between polynomial time frequency classes and selecti...

Measuring Concurrency of Regular Distributed Computations

In this paper, we present a concurrency measure that is especially adapted to distributed programs that exhibit regular run-time behaviours. Such programs are frequently obtained by automatic parallelization of sequential code. This measure is based on the antichain lattice of the partial order that models the distributed execution under consideration. We show under which condition the measure ...