Università degli Studi di Padova

“The Kleene tree and the construction of a computable function on the square with no computable fixed point (in practice)”

Martedì 22 Ottobre 2019, ore 16:30 - Aula 2AB45 - Petrus Potgieter (University of South Africa, visitor within our European project CID)


We consider the construction of the Baigger counter-example in constructive analysis for the Brouwer fixed-point theorem. There exists an actual (Polish school) computable function mapping the unit square to itself, all the fixed points of which are non-computable points and therefore algorithmically indeterminable. The algorithm computing the Baigger function uses the Kleene tree, a famous infinite computable tree which has no computable infinite path and giving an actual example of the tree (of which there are many equivalent) is part of the problem. We show how to do this using the exotic Fractran language, interpreted in Python. This allows definition of the Baigger function from the bottom up.

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