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- Denis R. Hirschfeldt, Carl G. Jockusch, Rutger Kuyper, Paul E. Schupp
- J. Symb. Log.
- 2016

A coarse description of a set A ⊆ ω is a set D ⊆ ω such that the symmetric difference of A and D has asymptotic density 0. We study the extent to which noncomputable information can be effectively recovered from all coarse descriptions of a given set A, especially when A is effectively random in some sense. We show that if A is 1-random and B is computable… (More)

- Laurent Bienvenu, Rutger Kuyper
- Computability and Complexity
- 2017

- Rutger Kuyper, Sebastiaan Terwijn
- Rew. Symb. Logic
- 2013

- Rutger Kuyper
- LFCS
- 2013

- Rutger Kuyper, Sebastiaan Terwijn
- J. Logic & Analysis
- 2014

We prove that a real x is 1-generic if and only if every differentiable computable function has continuous derivative at x. This provides a counterpart to recent results connecting effective notions of randomness with differentiability. We also consider multiply differentiable computable functions and polynomial time computable functions.

- Rutger Kuyper
- Arch. Math. Log.
- 2014

Skvortsova showed that there is a factor of the Medvedev lattice which captures intuitionistic propositional logic (IPC). However, her factor is unnatural in the sense that it is constructed in an ad hoc manner. We present a more natural example of such a factor. We also show that the theory of every non-trivial factor of the Medvedev lattice is contained… (More)

- Rutger Kuyper
- Ann. Pure Appl. Logic
- 2013

We give natural examples of factors of the Muchnik lattice which capture intuitionistic propositional logic (IPC), arising from the concepts of lowness, 1-genericity, hyperimmune-freeness and computable traceability. This provides a purely computational semantics for IPC.

- Rutger Kuyper
- Math. Log. Q.
- 2014

We consider the complexity of satisfiability in ε-logic, a probability logic. We show that for the relational fragment this problem is Σ 1 1-complete for rational ε ∈ (0, 1), answering a question by Terwijn. In contrast, we show that satisfiability in 0-logic is decidable. The methods we employ to prove this fact also allow us to show that 0-logic is… (More)

- Vasco Brattka, Rupert Hölzl, Rutger Kuyper
- STACS
- 2017

We introduce Monte Carlo computability as a probabilistic concept of computability on infinite objects and prove that Monte Carlo computable functions are closed under composition. We then mutually separate the following classes of functions from each other: the class of multi-valued functions that are non-deterministically computable, that of Las Vegas… (More)

- Uri Andrews, Rutger Kuyper, Steffen Lempp, Mariya Ivanova Soskova, Mars M. Yamaleev
- Computability and Complexity
- 2017