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The brouwer fixed point theorem revisited

par Brattka, Vasco;Le Roux, Stephane ;Miller, Joseph C.;Pauly, Arno
Référence Lecture notes in computer science, 9709, page (58-67)
Publication Publié, 2016

Article révisé par les pairs

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Résumé :

We revisit the investigation of the computational content of the Brouwer Fixed Point Theorem in [7], and answer the two open questions from that work. First, we show that the computational hardness is independent of the dimension, as long as it is greater than 1 (in [7] this was only established for dimension greater than 2). Second, we show that restricting the Brouwer Fixed Point Theorem to L-Lipschitz functions for any L > 1 also does not change the computational strength, which together with prior results establishes a trichotomy for L > 1, L = 1 and L < 1.