most citedSet theoretical Representations of Integers, I

3 citations · 5 across the 6 of their papers we have counts for

collaborators

6 papers

math.LO20081 cited

Kolmogorov complexity in perspective

Marie Ferbus-Zanda, Serge Grigorieff

We survey the diverse approaches to the notion of information content: from Shannon entropy to Kolmogorov complexity. The main applications of Kolmogorov complexity are presented n…

math.LO20083 cited

Set theoretical Representations of Integers, I

Marie Ferbus-Zanda, Serge Grigorieff

We reconsider some classical natural semantics of integers (namely iterators of functions, cardinals of sets, index of equivalence relations), in the perspective of Kolmogorov comp…

math.LO2008

Kolmogorov complexities Kmax, Kmin on computable partially ordered sets

Marie Ferbus-Zanda, Serge Grigorieff

We introduce a machine free mathematical framework to get a natural formalization of some general notions of infinite computation in the context of Kolmogorov complexity. Namely, t…

math.LO2008

Refinment of the "up to a constant" ordering using contructive co-immunity and alike. Application to the Min/Max hierarchy of Kolmogorov complexities

Marie Ferbus-Zanda, Serge Grigorieff

We introduce orderings between total functions f,g: N -> N which refine the pointwise "up to a constant" ordering <=cte and also insure that f(x) is often much less thang(x). With…

math.LO20081 cited

Church, Cardinal and Ordinal Representations of Integers and Kolmogorov complexity

Marie Ferbus-Zanda, Serge Grigorieff

We consider classical representations of integers: Church's function iterators, cardinal equivalence classes of sets, ordinal equivalence classes of totally ordered sets. Since pro…

math.LO2008

Is Randomness "Native" to Computer Science?

Marie Ferbus-Zanda, Serge Grigorieff

We survey the Kolmogorov's approach to the notion of randomness through the Kolmogorov complexity theory. The original motivation of Kolmogorov was to give up a quantitative defini…