Computability theory, also known as recursion theory, is a branch of mathematical logic, computer science, and the theory of computation that originated in the 1930s with the study of computable functions and Turing degrees.

2004年6月24日 · This was the beginning of the modern theory of computation. In this section we are dealing with complexity instead of computability, and all the Turing machines that we consider will halt on all their inputs.

Computability theory, also known as recursion theory, is the area of mathematics dealing with the concept of an effective procedure – a procedure that can be carried out by following specific rules.

Computability is the ability to solve a problem in an effective manner. It is a key topic of the field of computability theory within mathematical logic and the theory of computation within computer science. The computability of a problem is closely linked to …

In Chapter 1 we use a Kleene-style introduction to the class of computable functions, and we will discuss the recursion theorem, c.e. sets, Turing degrees, basic priority arguments, the existence of minimal degrees and a few other results.

The main prerequisite for the notes is knowledge of basic model theory: structures, isomorphisms and embeddings of them, compactness, and completeness. Starred sections are optional.

Topics include regular and context-free languages, decidable and undecidable problems, reducibility, recursive function theory, time and space measures on computation, completeness, hierarchy theorems, inherently complex problems, oracles, probabilistic computation, and interactive proof systems.

2023年8月7日 · Computability theory is the mathematical theory of algorithms, which explores the power and limitations of computation. Classical computability theory formalized the intuitive notion of an algorithm and provided a theoretical basis for digital computers.

Computability Theory Jose Emilio Alcantara Regio & Waseet Kazmi University of Connecticut December 9, 2020 1/40. Materials used Computability Theory, Rebecca Weber 2/40. Overview 1 Introduction 2 Capturing Computability 3 Computable Functions 4 Computable and Computably Enumerable Sets 5 Turing Reductions 6 Turing Degrees 3/40.

Computability Theory deals with what can and cannot be computed on a particular computing model. It does not make any claims on the number of steps required, or the amount of space required, to do the computation.