Information: - Mathematical logic is a subfield of mathematics exploring the applications of formal logic to mathematics. It bears close connections to metamathematics, the foundations of mathematics, and theoretical computer science. The unifying themes in mathematical logic include the study of the expressive power of formal systems and the deductive power of formal proof systems. Mathematical logic is often divided into the fields of set theory, model theory, recursion theory, and proof theory. These areas share basic results on logic, particularly first-order logic, and definability. In computer science (particularly in the ACM Classification) mathematical logic encompasses additional topics not detailed in this article; see Logic in computer science for those. - Computer science is the study of the theory, experimentation, and engineering that form the basis for the design and use of computers. It is the scientific and practical approach to computation and its applications and the systematic study of the feasibility, structure, expression, and mechanization of the methodical procedures (or algorithms) that underlie the acquisition, representation, processing, storage, communication of, and access to information. An alternate, more succinct definition of computer science is the study of automating algorithmic processes that scale. A computer scientist specializes in the theory of computation and the design of computational systems. - In computer science and mathematical logic the Turing degree (named after Alan Turing) or degree of unsolvability of a set of natural numbers measures the level of algorithmic unsolvability of the set. - Mathematics (from Greek "mathma", knowledge, study, learning) is the study of topics such as quantity (numbers), structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics. - Metalogic is the study of the metatheory of logic. Whereas "logic" studies how logical systems can be used to construct valid and sound arguments, metalogic studies the properties of logical systems. Logic concerns the truths that may be derived using a logical system; metalogic concerns the truths that may be derived "about" the languages and systems that are used to express truths. - In theoretical computer science and mathematics, the theory of computation is the branch that deals with how efficiently problems can be solved on a model of computation, using an algorithm. The field is divided into three major branches: automata theory and language, computability theory, and computational complexity theory, which are linked by the question: ""What are the fundamental capabilities and limitations of computers?"." - Computability theory, also called recursion theory, is a branch of mathematical logic, of computer science, and of the theory of computation that originated in the 1930s with the study of computable functions and Turing degrees. The field has since grown to include the study of generalized computability and definability. In these areas, recursion theory overlaps with proof theory and effective descriptive set theory. - Proof theory is a major branch of mathematical logic that represents proofs as formal mathematical objects, facilitating their analysis by mathematical techniques. Proofs are typically presented as inductively-defined data structures such as plain lists, boxed lists, or trees, which are constructed according to the axioms and rules of inference of the logical system. As such, proof theory is syntactic in nature, in contrast to model theory, which is semantic in nature. - Effective descriptive set theory is the branch of descriptive set theory dealing with sets of reals having lightface definitions; that is, definitions that do not require an arbitrary real parameter (Moschovakis 1980). Thus effective descriptive set theory combines descriptive set theory with recursion theory. - In logic, mathematics and computer science, especially metalogic and computability theory, an effective method or effective procedure is a procedure for solving a problem from a specific class. An effective method is sometimes also called mechanical method or procedure. - In theoretical computer science, a computational problem is a mathematical object representing a collection of questions that computers might be able to solve. For example, the problem of factoring - Theoretical computer science, or TCS, is a division or subset of general computer science and mathematics that focuses on more abstract or mathematical aspects of computing and includes the theory of computation. - In mathematics and computer science, an algorithm is a self-contained sequence of actions to be performed. Algorithms perform calculation, data processing, and/or automated reasoning tasks. - Computable functions are the basic objects of study in computability theory. Computable functions are the formalized analogue of the intuitive notion of algorithm, in the sense that a function is computable if there exists an algorithm that can do the job of the function, i.e. given an input of the function domain it can return the corresponding output. Computable functions are used to discuss computability without referring to any concrete model of computation such as Turing machines or register machines. Any definition, however, must make reference to some specific model of computation but all valid definitions yield the same class of functions. Particular models of computability that give rise to the set of computable functions are the Turing-computable functions and the -recursive functions. - In computability theory and computational complexity theory , a decision problem is a question in some formal system with a yes - or - no answer , depending on the values of some input parameters . Decision problems typically appear in mathematical questions of decidability , that is , the question of the existence of an effective method to determine the existence of some object or its membership in a set ; some of the most important problems in mathematics are undecidable . For example , the problem '' given two numbers x and y , does x evenly divide y ? '' is a decision problem . The answer can be either ' yes ' or ' no ' , and depends upon the values of x and y. A method for solving a decision problem , given in the form of an algorithm , is called a decision procedure for that problem . A decision procedure for the decision problem '' given two numbers x and y , does x evenly divide y ? '' would give the steps for determining whether x evenly divides y , given x and y. One such algorithm is long division , taught to many school children . If the remainder is zero the answer produced is ' yes ' , otherwise it is ' no ' . A decision problem which can be solved by an algorithm , such as this example , is called decidable . The field of computational complexity categorizes decidable decision problems by how difficult they are to solve . '' Difficult '' , in this sense , is described in terms of the computational resources needed by the most efficient algorithm for a certain problem . The field of recursion theory , meanwhile , categorizes undecidable decision problems by Turing degree , which is a measure of the noncomputability inherent in any solution . Decision problems are closely related to function problems , which can have answers that are more complex than a simple ' yes ' or ' no ' . A corresponding function problem is '' given two numbers x and y , what is x divided by y ? '' . They are also related to optimization problems , which are concerned with finding the best answer to a particular problem .... - Complexity describes the behaviour of a system or model whose components interact in multiple ways and follow local rules, meaning there is no reasonable higher instruction to define the various possible interactions. - Computational complexity theory is a branch of the theory of computation in theoretical computer science that focuses on classifying computational problems according to their inherent difficulty, and relating those classes to each other. A computational problem is understood to be a task that is in principle amenable to being solved by a computer, which is equivalent to stating that the problem may be solved by mechanical application of mathematical steps, such as an algorithm. - A formal system or logical calculus is any well-defined system of abstract thought based on the model of mathematics. A formal system need not be mathematical as such; for example, Spinoza's "Ethics" imitates the form of Euclid's "Elements".. Spinoza employed Euclidiean elements such as "axioms" or "primitive truths", rules of inferences etc. so that a calculus can be build using these. For nature of such primitive truths, one can consult Tarski's "Concept of truth for a formalized language". - An axiom or postulate is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments. The word comes from the Greek "axima" 'that which is thought worthy or fit' or 'that which commends itself as evident.' - Set theory is a branch of mathematical logic that studies sets, which informally are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics. The language of set theory can be used in the definitions of nearly all mathematical objects. - Truth is most often used to mean being in accord with fact or reality, or fidelity to an original or standard. Truth may also often be used in modern contexts to refer to an idea of "truth to self," or authenticity. - A computer is a device that can be instructed to carry out an arbitrary set of arithmetic or logical operations automatically. The ability of computers to follow a sequence of operations, called a "program", make computers very flexible and useful. Such computers are used as control systems for a very wide variety of industrial and consumer devices. This includes simple special purpose devices like microwave ovens and remote controls, factory devices such as industrial robots and computer assisted design, but also in general purpose devices like personal computers and mobile devices such as smartphones. The Internet is run on computers and it connects millions of other computers. What object entity has the relation of 'subclass of' with the subject 'decision problem'? Choices: - ability - analysis - axiom - being - branch - calculation - calculus - collection - computational problem - computer - computing - concept - data - definition - design - device - engineering - factory - field - function - general - greek - idea - information - job - learning - logic - logical system - mathematical logic - mathematics - model - model theory - natural - object - order - out - postulate - power - question - range - reasoning - representation - scale - science - scientist - sense - sequence - set - set theory - sound - statement - storage - study - subset - system - theory - thought - type - word
The answer to this question is:
computational problem