10 citations · 21 across the 10 of their papers we have counts for
10 papers
Rigorous Function Calculi in Ariadne
Pieter Collins, Luca Geretti, Sanja Zivanovic Gonzalez +2
Almost all problems in applied mathematics, including the analysis of dynamical systems, deal with spaces of real-valued functions on Euclidean domains in their formulation and sol…
Computable Random Variables and Conditioning
Pieter Collins
The aim of this paper is to present an elementary computable theory of random variables, based on the approach to probability via valuations. The theory is based on a type of lower…
Higher Order Method for Differential Inclusions
Sanja Zivanovic Gonzalez, Pieter Collins, Luca Geretti +2
Uncertainty is unavoidable in modeling dynamical systems and it may be represented mathematically by differential inclusions. In the past, we proposed an algorithm to compute valid…
Semantics, Specification Logic, and Hoare Logic of Exact Real Computation
Sewon Park, Franz Brauße, Pieter Collins +7
We propose a simple imperative programming language, ERC, that features arbitrary real numbers as primitive data type, exactly. Equipped with a denotational semantics, ERC provides…
Computable Stochastic Processes
Pieter Collins
The aim of this paper is to present an elementary computable theory of probability, random variables and stochastic processes. The probability theory is baed on existing approaches…
Higher Order Methods for Differential Inclusions
Sanja Gonzalez Zivanovic, Pieter Collins
We present a numerical method for rigorous over-approximation of a reachable set of differential inclusions. The method gives high-order error bounds for single step approximations…