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Rankings as ordinal scale measurement results

100%

Muravyov S. V.

tom Vol. 14, nr 1

9-23

Rankings (or preference relations, or weak orders) are sometimes considered to be non-empirical, non-objective, low-informative and, in principle, are not worthy to be titled measurements. A purpose of the paper is to demonstrate that the measurement result on the ordinal scale should be an entire (consensus) ranking of n objects ranked by m properties (or experts, or voters) in order of preference and the ranking is one of points of the weak orders space. The consensus relation that would give an integrative characterization of the initial rankings is one of strict (linear) order relations, which, in some sense, is nearest to every of the initial rankings. A recursive branch and bound measurement procedure for finding the consensus relation is described. An approach to consensus relation uncertainty assessment is discussed.

A Behavioural Theory of Recursive Algorithms

88%

Börger E. , Schewe K.-D.

Fundamenta Informaticae

2020

tom Vol. 177, nr 1

1--37

“What is an algorithm?” is a fundamental question of computer science. Gurevich’s behavioural theory of sequential algorithms (aka the sequential ASM thesis) gives a partial answer by defining (non-deterministic) sequential algorithms axiomatically, without referring to a particular machine model or programming language, and showing that they are captured by (non-deterministic) sequential Abstract State Machines (nd-seq ASMs). However, recursive algorithms such as mergesort are not covered by this theory, as has been pointed out by Moschovakis, who had independently developed a different framework to mathematically characterize the concept of (in particular recursive) algorithm. In this article we propose an axiomatic definition of the notion of sequential recursive algorithm which extends Gurevich’s axioms for sequential algorithms by a Recursion Postulate and allows us to prove that sequential recursive algorithms are captured by recursive Abstract State Machines, an extension of nd-seq ASMs by a CALL rule. Applying this recursive ASM thesis yields a characterization of sequential recursive algorithms as finitely composed concurrent algorithms all of whose concurrent runs are partial-order runs.