Affine functions and series with co-inductive real numbers

Affine functions and series with co-inductive real numbers

We extend the work of A. Ciaffaglione and P. di Gianantonio on mechanical verification of algorithms for exact computation on real numbers, using infinite streams of digits implemented as a co-inductive type. Four aspects are studied: the first aspect concerns the proof that digit streams can be related to axiomatized real numbers when they are already present in the proof system. The second as...

Inductive Inference of Real Functions

Characterizing Global Minimizers of the Difference of Two Positive Valued Affine Increasing and Co-radiant Functions

‎Many optimization problems can be reduced to a problem with an increasing and co-radiant objective function by a suitable transformation of variables. Functions, which are increasing and co-radiant, have found many applications in microeconomic analysis. In this paper, the abstract convexity of positive valued affine increasing and co-radiant (ICR) functions are discussed. Moreover, the ...

Feasible Functions over Co-inductive Data

Proof theoretic characterizations of complexity classes are of considerable interest because they link levels of conceptual abstraction to computational complexity. We consider here the provability of functions over coinductive data in a highly expressive, yet proof-theoretically weak, variant of second order logic L ∗ , which we believe captures the notion of feasibility more broadly than prev...

Belief functions on real numbers

We generalize the TBM (transferable belief model) to the case where the frame of discernment is the extended set of real numbersR = [−∞,∞], under the assumptions that ‘masses’ can only be given to intervals. Masses become densities, belief functions, plausibility functions and commonality functions become integrals of these densities and pignistic probabilities become pignistic densities. The m...