Formalism and intuition in computability

Formalism and intuition in computability.

The model of recursive functions in 1934-1936 was a deductive formal system. In 1936, Turing and in 1944, Post introduced more intuitive models of Turing machines and generational systems. When they both died prematurely in 1954, their informal approach was replaced again by the very formal Kleene T-predicate for another decade. By 1965, researchers could no longer read the papers. A second wav...

Religious Experience and Mystical Intuition Structurally Compared

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L1-Computability, Layerwise Computability and Solovay Reducibility

We propose a hierarchy of classes of functions that corresponds to the hierarchy of randomness notions. Each class of functions converges at the corresponding random points. We give various characterizations of the classes, that is, characterizations via integral tests, L-computability and layerwise computability. Furthermore, the relation among these classes is formulated using a version of So...

Intuition and the Axiomatic Method Intuition and the Axiomatic Method

Computability and Non-computability Issues in Amorphous Computing

Amorphous computing systems consist of a huge set of tiny simple stationary or mobile processors whose computational, communication and sensory part is reduced to an absolute minimum. In an airborne medium the processors communicate via a short-range radio while in a waterborne medium via molecular communication. In some cases the computational part of the processors can be simplified down to f...