Computability by Normal Algorithms

CSE200: Computability and complexity Randomized algorithms

Applicability conditions for plans with loops: Computability results and algorithms

The utility of including loops in plans has been long recognized by the planning community. Loops in a plan help increase both its applicability and the compactness of representation. However, progress in finding such plans has been limited largely due to lack of methods for reasoning about the correctness and safety properties of loops of actions. We present novel algorithms for determining th...

Expressing Algorithms as Concise as Possible via Computability Logic

This paper proposes a new approach to defining and expressing algorithms: the notion of task logical algorithms. This notion allows the user to define an algorithm for a task T as a set of agents who can collectively perform T . This notion considerably simplifies the algorithm development process and can be seen as an integration of the sequential pseudocode and logical algorithms. This observ...

Axiomatic Theory of Algorithms: Computability and Decidability in Algorithmic Classes

Axiomatic approach has demonstrated its power in mathematics. The main goal of this paper is to show that axiomatic methods are also very efficient for computer science. It is possible to apply these methods to many problems in computer science. Here the main modes of computer functioning and program execution are described, formalized, and studied in an axiomatic context. The emphasis is on th...

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...