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Computational Problems in Metric Fixed Point Theory and their Weihrauch Degrees

Eike Neumann.

We study the computational difficulty of the problem of finding fixed points of nonexpansive mappings in uniformly convex Banach spaces. We show that the fixed point sets of computable nonexpansive self-maps of a nonempty, computably weakly closed, convex and bounded subset of a computable real&nbsp;[&hellip;]

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Computability in Basic Quantum Mechanics

Eike Neumann ; Martin Pape ; Thomas Streicher.

The basic notions of quantum mechanics are formulated in terms of separable infinite dimensional Hilbert space $\mathcal{H}$. In terms of the Hilbert lattice $\mathcal{L}$ of closed linear subspaces of $\mathcal{H}$ the notions of state and observable can be formulated as kinds of measures as in&nbsp;[&hellip;]

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Uniform Envelopes

Eike Neumann.

In the author's PhD thesis (2019) universal envelopes were introduced as a tool for studying the continuously obtainable information on discontinuous functions. To any function $f \colon X \to Y$ between $\operatorname{qcb}_0$-spaces one can assign a so-called universal envelope which, in a&nbsp;[&hellip;]

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Decision problems for linear recurrences involving arbitrary real numbers

Eike Neumann.

We study the decidability of the Skolem Problem, the Positivity Problem, and the Ultimate Positivity Problem for linear recurrences with real number initial values and real number coefficients in the bit-model of real computation. We show that for each problem there exists a correct partial&nbsp;[&hellip;]

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Semantics, Specification Logic, and Hoare Logic of Exact Real Computation

Sewon Park ; Franz Brauße ; Pieter Collins ; SunYoung Kim ; Michal Konečný ; Gyesik Lee ; Norbert Müller ; Eike Neumann ; Norbert Preining ; Martin Ziegler.

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 a formal programming language-theoretic foundation to the algorithmic processing of real numbers. In order to capture&nbsp;[&hellip;]

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