We consider the descriptive complexity of some subsets of the infinite permutation group S∞ which arise naturally from the classical series rearrangement theorems of Riemann, Levy, and Steinitz. In particular, given some fixed conditionally convergent series of vectors in Euclidean space Rd, we study the set of permutations which make the series diverge, as well as the set of permutations which...

There is a growing need for abstractions in logic specification languages such as FO(·) and ASP. One technique to achieve these abstractions are templates (sometimes called macros). While the semantics of templates are virtually always described through a syntactical rewriting scheme, we present an alternative view on templates as second order definitions. To extend the existing definition cons...

We construct a minimal rK-degree, continuum many, in fact. We also show that every minimal sequence, that is, a sequence with minimal rK-degree, must have very low descriptional complexity, that every minimal sequence is rK-reducible to a random sequence, and that there is a random sequence with no minimal sequence rK-reducible to it.

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In this paper we develop a computational framework for the measurement of different factors or abilities which are usually found in intelligent behaviours. For this, we first develop a scale for measuring the complexity of an instance of a problem, depending on the descriptional complexity (Levin LT variant) of the ‘explanation’ of the answer to the problem. We centre on the establishment of ei...

Background and purpose: Utilization of health care services and food influence the health status. The food and health care expenditure ratios determine the importance level of them in household's consumption expenditures. We aimed to investigate the Iranian rural and urban food and health expenditure ratios inequality during 1998 to 2012. Materials and Methods: This is a descriptive longitudina...

Modeling provides a bridge between the natural sciences (physics, chemistry, biology, and the like) and the axiomatic sciences (mathematics and statistics). Inductively-derived descriptive models map observations of physical processes into mathematical descriptions that can be treated as axioms (e.g., the various laws of physics). A synthetic model combines descriptive models of several physica...