Contextual Insertions/Deletions and Computability

Contextual Insertions/Deletions and Computability

We investigate two generalizations of insertion and deletion of words, that have recently become of interest in the context of molecular computing. Given a pair of words (x, y), called a context, the (x, y)-contextual insertion of a word v into a word u is performed as follows. For each occurrence of xy as a subword in u, we include in the result of the contextual insertion the words obtained b...

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...

Ordered Structures and Computability Ordered Structures and Computability Dedication

We consider three questions surrounding computable structures and orderings. First, we make progress toward answering a question of Downey, Hirschfeldt, and Goncharov by showing that for a large class of countable linear orderings, the Turing degree spectrum of the successor relation is closed upward in the c.e. degrees. Next we consider computable partial orders (specifically, finitely branchi...

Computability versus exact computability of martingales

This note gives a simple example of a polynomial time computable martingale that has rational values but is not exactly computable.

Computability and Logic