halting problem

Cognitivism has been criticised in a number of ways. Phenomenologists and hermeneutic philosophers have criticised the positivist approach of cognitivism for reducing individual meaning to what they perceive as measurements stripped of all significance. They argue that by representing experiences and mental functions as measurements, cognitivism is ignoring the context (cf contextualism) and, therefore, the meaning of these measurements. They believe that it is this personal meaning of experience gained from the phenomenon as it is ex ...

See also:

Cognitivism psychology, Cognitivism psychology - Theoretical approach, Cognitivism psychology - Criticisms of psychological cognitivism

Read more here: » Cognitivism psychology: Encyclopedia II - Cognitivism psychology - Criticisms of psychological cognitivism

More formally, a decision problem is a problem that takes as input some string and requires as output either YES or NO. If there is an algorithm (say a Turing machine, or a LISP or Pascal program with unbounded memory) which is able to produce the correct answer for any input string of length n in at most nk steps, where k is some constant independent of the input string, then we say that the problem can be solved in polynomial time and we place it in the class P. Intuitively, we think of the pr ...

See also:

Complexity classes P and NP, Complexity classes P and NP - Formal definitions, Complexity classes P and NP - NP-complete, Complexity classes P and NP - Still harder problems, Complexity classes P and NP - Is P really tractable?, Complexity classes P and NP - Why do computer scientists think P ≠ NP?, Complexity classes P and NP - Results about difficulty of proof, Complexity classes P and NP - Polynomial-time algorithms, Complexity classes P and NP - Logical characterizations, Complexity classes P and NP - Trivia

Read more here: » Complexity classes P and NP: Encyclopedia II - Complexity classes P and NP - Formal definitions

Cantor's diagonal argument is a proof devised by Georg Cantor to demonstrate that the real numbers are not countably infinite. (It is also called the diagonalization argument or the diagonal slash argument or the diagonal method.) The diagonal argument was not Cantor's first proof of the uncountability of the real numbers, but was published three years after his first proof. His original argument did not mention decimal expansions, nor any other numeral system. Since this technique was first used, si ...

Including:

• Cantor's diagonal argument - Real numbers
• Cantor's diagonal argument - Why this does not work on integers
• Cantor's diagonal argument - General sets

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Alonzo Church (June 14, 1903 – August 11, 1995) was an American mathematician and logician who was responsible for some of the foundations of theoretical computer science. Born in Washington, DC, he received a bachelor's degree from Princeton University in 1924, completing his Ph.D. there in 1927, under Oswald Veblen. After a postdoc at Göttingen, he taught at Princeton, 1929-67, and at ...

Including:

• Alonzo Church - Death
• Alonzo Church - Books

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In the computer science subfield of algorithmic information theory the Chaitin constant or halting probability is a construction by Gregory Chaitin which describes the probability that a randomly generated program for a given model of computation or programming language will halt. It is usually denoted . It is a normal and transcendental number which can be defined but cannot be computed. This means one can prove ...

Including:

• Chaitin's constant - Definition
• Chaitin's constant - Notes
• Chaitin's constant - Calculation of the start of a Chaitin

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Computational complexity theory is part of the theory of computation dealing with the resources required during computation to solve a given problem. The most common resources are time (how many steps does it take to solve a problem) and space (how much memory does it take to solve a problem). In this theory, the class P consists of all those decision problems that can be solved on a deterministic sequential machine in an amount of time that is polynomial in the size of the input; the class NP consists of all those decis ...

Including:

• Complexity classes P and NP - Formal definitions
• Complexity classes P and NP - NP-complete
• Complexity classes P and NP - Still harder problems
• Complexity classes P and NP - Is P really tractable?
• Complexity classes P and NP - Why do computer scientists think P ≠ NP?
• Complexity classes P and NP - Results about difficulty of proof
• Complexity classes P and NP - Polynomial-time algorithms
• Complexity classes P and NP - Logical characterizations
• Complexity classes P and NP - Trivia

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In mathematics and computer science an algorithm is a finite set of well-defined instructions for accomplishing some task which, given an initial state, will terminate in a corresponding recognizable end-state. Algorithms can be implemented by computer programs. Informally, the concept of an algorithm is often illustrated by the example of a recipe, although many algorithms are much more complex; algorithms often have steps that repeat (iterate) or require decisions (such as logic or comparison). The concept of algorithms was formalized in 1936 by Alan Turing's Turing machines and Alonzo Church's lambda c ...

Including:

• Algorithm - Formalization of algorithms
• Algorithm - Implementation
• Algorithm - Example
• Algorithm - History
• Algorithm - Classes
• Algorithm - Classification by implementation
• Algorithm - Classification by design paradigm
• Algorithm - Classification by field of study
• Algorithm - Classification by complexity
• Algorithm - Sources
• Algorithm - Legal issues

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In psychology, cognitivism is a theoretical approach to understanding the mind, which argues that mental function can be understood by quantitative, positivist and scientific methods, and that such functions can be described as information processing models. Cognitivism psychology - Theoretical approach. Cognitivism has two major components, one methodological, the other theoretical. Methodologically, cognitivism adopts a positivist approach and the belief that psychology can be (in principle) fully explain ...

Including:

• Cognitivism psychology - Theoretical approach
• Cognitivism psychology - Criticisms of psychological cognitivism

Read more here: » Cognitivism psychology: Encyclopedia - Cognitivism psychology

Zero day or 0day refers to software, media, or information that is obtained either slightly prior to or on the day of the official release. Items gained further in advance are deemed "Negative day" or sometimes "-day". Zero day - Zero day warez. When applied to copyrighted works such as computer software, motion pictures, and musical recordings, zero day has connotations of illegality. Zero day software is warez, that is, infringing items. The term derives from the day when the software is il ...

Including:

• Zero day - Zero day warez
• Zero day - Zero day vulnerabilities

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Advice is a concept in complexity theory. An advice string is an extra input to a Turing machine which is allowed to depend on the length n of the input, but not on input itself. A decision problem is in the complexity class P/f(n) if there is a polynomial time Turing machine M with the following property: for any n, there is an advice string A of length f(n) such that, for any input x of length n, the machine M correctly decides the p ...

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Infinity is a term with very distinct, separate meanings which arise in theology, philosophy, mathematics and everyday life. Popular or colloquial usage of the term often does not accord with its more technical meanings. The word infinity comes from Latin : "Infinito", unending. In theology, for example in the work of theologians such as Duns Scotus, the infinite nature of God invokes a sense of being without constraint, rather than a sense of being unlimited in quantity. In philosophy, infinity can be attrib ...

Including:

• Infinity - History
• Infinity - Ancient view of infinity
• Infinity - Views from the Renaissance to modern times
• Infinity - Modern philosophical views
• Infinity - Infinity symbol
• Infinity - Mathematical infinity
• Infinity - Infinity in real analysis
• Infinity - Infinity in complex analysis
• Infinity - Arithmetic properties of infinity
• Infinity - Infinity in set theory
• Infinity - Mathematics without infinity
• Infinity - Use of infinity in common speech
• Infinity - Physical infinity
• Infinity - Infinity in cosmology
• Infinity - Three types of infinities
• Infinity - Infinity in science fiction
• Infinity - Note

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In computer science, Abstract interpretation is a theory of sound approximation of the semantics of computer programs, based on monotonic functions over ordered sets, especially lattices. It can be viewed as a partial execution of a computer program which gains information about its semantics (e.g. control structure, flow of information) without performing all the calculations. Its main concrete application is formal static analysis, the automatic extraction of information about the possible executions of computer programs; suc ...

Including:

• Abstract interpretation - Intuition
• Abstract interpretation - Abstract interpretation of computer programs
• Abstract interpretation - Formalization
• Abstract interpretation - Examples of abstract domains
• Abstract interpretation - Tools

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Information theory is the mathematical theory of data communication and storage, generally considered to have been founded in 1948 by Claude E. Shannon. The central paradigm of classic information theory is the engineering problem of the transmission of information over a noisy channel. The most fundamental results of this theory are Shannon's source coding theorem, which establishes that on average the number of bits needed to communicate the result of an uncertain event is given by the entropy of that uncertainty; and ...

Including:

• Information theory - Mathematical preliminaries
• Information theory - Basic Concepts for Discrete Channels
• Information theory - Self-information
• Information theory - Entropy
• Information theory - Joint Entropy
• Information theory - Conditional Entropy Equivocation
• Information theory - Mutual Information Transinformation
• Information theory - Continuous Channels
• Information theory - Channel Capacity
• Information theory - Source Theory
• Information theory - Rate
• Information theory - Fundamental Theorem
• Information theory - Statement Noisy-Channel Coding Theorem
• Information theory - Channel capacity of particular model channels
• Information theory - Related Concepts
• Information theory - Measure Theory
• Information theory - Kolmogorov Complexity
• Information theory - Applications
• Information theory - Coding Theory
• Information theory - Cryptography Cryptanalysis
• Information theory - Relation with thermodynamic entropy
• Information theory - Quantum Information Theory
• Information theory - Detection and Estimation Theory
• Information theory - Gambling
• Information theory - Intelligence
• Information theory - Music
• Information theory - History

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The soul, according to many religious and philosophical traditions, is the ethereal substance — spirit (Hebrew:rooah or nefesh) — particular to a unique living being. Such traditions often consider the soul both immortal and innately aware of its immortal nature, as well as the true basis for sentience in each living being. The concept of the soul has strong links with notions of an afterlife, but opinions may vary wildly, even within a given religion, as to what happens to the soul after death. Many wi ...

Including:

• Soul - Etymologies
• Soul - Philosophical views
• Soul - Socrates and Plato
• Soul - Aristotle
• Soul - Religious views
• Soul - Bahá'í beliefs
• Soul - Buddhist beliefs
• Soul - Christian beliefs
• Soul - Hindu beliefs
• Soul - Islamic beliefs
• Soul - Jainist beliefs
• Soul - Jewish beliefs
• Soul - Other religious beliefs and views
• Soul - Science and the soul
• Soul - Materialistic Science and the Soul
• Soul - Scientific approaches for study of a non-material soul
• Soul - Other uses of the term
• Soul - Movie
• Soul - External references and links

Read more here: » Soul: Encyclopedia - Soul

Alan Mathison Turing (June 23, 1912 – June 7, 1954) was a British mathematician, logician, and cryptographer. Turing is often considered to be a father of modern computer science. With the Turing Test, he made a significant and characteristically provocative contribution to the debate regarding artificial intelligence: whether it will ever be possible to say that a machine is conscious and can think. He provided an influential formalisation of the concept of algorithm and computation with the Turing machine, formulating the n ...

Including:

• Alan Turing - Childhood and youth
• Alan Turing - College and his work on computability
• Alan Turing - Cryptanalysis
• Alan Turing - Work on early computers and the Turing Test
• Alan Turing - Work on pattern formation and mathematical biology
• Alan Turing - Prosecution for homosexuality and Turing's death
• Alan Turing - Recognition
• Alan Turing - Turing biographies
• Alan Turing - Turing in fiction

Read more here: » Alan Turing: Encyclopedia - Alan Turing

In everyday use, the correctness of a statement is determined by whether or not it matches reality. People can think a statement is correct and be wrong. When scoring tests of knowledge where there is only one accepted answer for each problem, a device or person marks an answer as correct if it matches what the test designer has determined the testee should answer. It is common for one or more answers, thought at the time by the designer of a test to match reality, and to, at a later date, be shown to not match what can be observed, a ...

Read more here: » Correctness: Encyclopedia - Correctness

A deadlock is a situation wherein two or more competing actions are waiting for the other to finish, so neither ever does. It is often seen in a paradox, like 'the chicken or the egg'. In the computing world deadlock refers to a specific condition when two processes are each waiting for the other to release a resource, or more than two processes are waiting for resources in a circular chain (see Necessary conditions). Deadlocks are a common problem in multiprocessing w ...

Including:

• Deadlock - Necessary conditions
• Deadlock - Deadlock avoidance
• Deadlock - Deadlock prevention
• Deadlock - Deadlock detection
• Deadlock - Distributed deadlocks
• Deadlock - Livelock

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Often we find ourselves trying to solve a problem that is similar to a problem we've already solved. In these cases, often a quick way of solving the new problem is to transform each instance of the new problem into instances of the old problem, solve these using our existing solution, and then use these to obtain our final solution. This is perhaps the most obvious use of reductions. Another, more subtle use is this: suppose we have a problem that we've proven is hard to solve, and we have a similar new problem. We might suspect that ...

See also:

Reduction complexity, Reduction complexity - Gentle Introduction, Reduction complexity - Definition, Reduction complexity - Examples, Reduction complexity - Detailed Example, Reduction complexity - Notes, Reduction complexity - Types and applications of reductions

Read more here: » Reduction complexity: Encyclopedia II - Reduction complexity - Gentle Introduction

The most common proof for the undecidability of PCP describes an instance of PCP that can simulate the computation of a Turing machine on a particular input. A match will only occur if the input would be accepted by the Turing machine. Because deciding if a Turing machine will accept an input is a basic undecidable problem, PCP cannot be decidable either. The following discussion is based on the proof from section 5.2 of Micha ...

See also:

Post correspondence problem, Post correspondence problem - Definition of the problem, Post correspondence problem - Example of an instance of the problem, Post correspondence problem - Proof sketch of undecidability, Post correspondence problem - Variants

Read more here: » Post correspondence problem: Encyclopedia II - Post correspondence problem - Proof sketch of undecidability

Given a Gödel numbering of the computable functions then for any property φ( − 1)[F] is recursive if and only if or . ...

See also:

Rice's theorem, Rice's theorem - Formal statement, Rice's theorem - Examples, Rice's theorem - Proof, Rice's theorem - Proof sketch, Rice's theorem - Formal proof

Read more here: » Rice's theorem: Encyclopedia II - Rice's theorem - Formal statement