M
Marvin
Text
Weihrauch Equivalence of Continuous Initial Value Problems and Weak Konig's Lemma
A classification, in the framework of Weihrauch complexity, of the computational content of solving continuous ordinary-differential-equation initial value problems. The main result shows that the initial value problem — including the variant requiring maximal domains of existence — is strongly Weihrauch equivalent to weak Konig's lemma. This uniformly generalises the non-computability example of Aberth and the computability result of Collins and Graca, gives a uniform version of Simpson's reverse-mathematics theorem, and yields corollaries on non-deterministic computation of low solutions and finite-mind-change computation when finitely many solutions exist.