# Glossari

Aquest glossari és una mostra dels termes més representatius d'Alan Turing. Les definicions han estat extretes dels recursos següents:

Vikipedia en català (VIKIPEDIA-CA)

Wikipedia en anglès (WIKIPEDIA-EN)

Wikipedia en castellà (WIKIPEDIA-ES)

Wolfram Science (WOLFRAM)

#### Artificial intelligence

Artificial intelligence (AI) is the intelligence exhibited by machines or software. It is also the name of the academic field of study which studies how to create computers and computer software that are capable of intelligent behavior. Major AI researchers and textbooks define this field as "the study and design of intelligent agents", in which an intelligent agent is a system that perceives its environment and takes actions that maximize its chances of success. John McCarthy, who coined the term in 1955, defines it as "the science and engineering of making intelligent machines".

Citació: " Artificial intelligence" A: *Wikipedia*. Wikimedia Foundation, 2011. [en línia]. [Consulta: 16 setembre 2015]. Disponible a: <https://en.wikipedia.org/wiki/Artificial_intelligence>

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#### Bletchley Park

Bletchley Park, in Milton Keynes, Buckinghamshire, England, was the central site of the United Kingdom's Government Code and Cypher School (GC&CS), which during the Second World War regularly penetrated the secret communications of the Axis Powers – most importantly the German Enigma and Lorenz ciphers. The official historian of World War II British Intelligence has written that the "Ultra" intelligence produced at Bletchley shortened the war by two to four years, and that without it the outcome of the war would have been uncertain.[1] The site is now an educational and historical attraction memorialising and celebrating those accomplishments.

Citació: "Bletchley Park" A: *Wikipedia*. Wikimedia Foundation, 2011. [en línia]. [Consulta: 16 setembre 2015]. Disponible a: <https://en.wikipedia.org/wiki/Bletchley_Park>

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#### Computing

Computing is any goal-oriented activity requiring, benefiting from, or creating algorithmic processes—e.g. through computers. Computing includes designing, developing and building hardware and software systems; processing, structuring, and managing various kinds of information; doing scientific research on and with computers; making computer systems behave intelligently; and creating and using communications and entertainment media. The field of computing includes computer engineering, software engineering, computer science, information systems, and information technology.

Citació: "Computing" A: *Wikipedia*. Wikimedia Foundation, 2011. [en línia]. [Consulta: 16 setembre 2015]. Disponible a:

<https://en.wikipedia.org/wiki/Computing>

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#### Cryptanalysis

Cryptanalysis (from the Greek kryptós, "hidden", and analýein, "to loosen" or "to untie") is the study of analyzing information systems in order to study the hidden aspects of the systems. Cryptanalysis is used to breach cryptographic security systems and gain access to the contents of encrypted messages, even if the cryptographic key is unknown.

In addition to mathematical analysis of cryptographic algorithms, cryptanalysis includes the study of side-channel attacks that do not target weaknesses in the cryptographic algorithms themselves, but instead exploit weaknesses in their implementation.

Even though the goal has been the same, the methods and techniques of cryptanalysis have changed drastically through the history of cryptography, adapting to increasing cryptographic complexity, ranging from the pen-and-paper methods of the past, through machines like the British Bombes and Colossus computers at Bletchley Park in World War II, to the mathematically advanced computerized schemes of the present. Methods for breaking modern cryptosystems often involve solving carefully constructed problems in pure mathematics, the best-known being integer factorization.

Citació: "Crytanalysis" A: *Wikipedia*. Wikimedia Foundation, 2011. [en línia]. [Consulta: 16 setembre 2015]. Disponible a:

<https://en.wikipedia.org/wiki/Cryptanalysis>

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#### Cryptography or cryptology

Cryptography or cryptology; from Greek κρυπτός kryptós, "hidden, secret"; and γράφειν graphein, "writing", or -λογία -logia, "study", respectively is the practice and study of techniques for secure communication in the presence of third parties (called adversaries). More generally, it is about constructing and analyzing protocols that block adversaries; various aspects in information security such as data confidentiality, data integrity, authentication, and non-repudiation are central to modern cryptography. Modern cryptography exists at the intersection of the disciplines of mathematics, computer science, and electrical engineering. Applications of cryptography include ATM cards, computer passwords, and electronic commerce.

Citació: "Cryptography" A:* Wikipedia*. Wikimedia Foundation, 2011. [en línia]. [Consulta: 16 setembre 2015]. Disponible a:

<https://en.wikipedia.org/wiki/Cryptography>

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#### Enigma machine

An Enigma machine was a series of electro-mechanical rotor cipher machines developed and used in the early to early-mid twentieth century for commercial and military usage. Enigma was invented by the German engineer Arthur Scherbius at the end of World War I. Early models were used commercially from the early 1920s, and adopted by military and government services of several countries, most notably Nazi Germany before and during World War II. Several different Enigma models were produced, but the German military models are the most commonly recognised.

Citació: "Enigma machine" A: *Wikipedia*. Wikimedia Foundation, 2011. [en línia]. [Consulta: 16 setembre 2015]. Disponible a: <https://en.wikipedia.org/wiki/Enigma_machine>

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#### Entscheidungsproblem

In mathematics and computer science, the Entscheidungsproblem (pronounced [ɛntˈʃaɪ̯dʊŋspʁoˌbleːm], German for 'decision problem') is a challenge posed by David Hilbert in 1928. The Entscheidungsproblem asks for an algorithm that takes as input a statement of a first-order logic (possibly with a finite number of axioms beyond the usual axioms of first-order logic) and answers "Yes" or "No" according to whether the statement is universally valid, i.e., valid in every structure satisfying the axioms. By the completeness theorem of first-order logic, a statement is universally valid if and only if it can be deduced from the axioms, so the Entscheidungsproblem can also be viewed as asking for an algorithm to decide whether a given statement is provable from the axioms using the rules of logic.

In 1936, Alonzo Church and Alan Turing published independent papers showing that a general solution to the Entscheidungsproblem is impossible, assuming that the intuitive notion of "effectively calculable" is captured by the functions computable by a Turing machine (or equivalently, by those expressible in the lambda calculus). This assumption is now known as the Church–Turing thesis.

Citació: "Entscheidungsproblem" A: *Wikipedia*. Wikimedia Foundation, 2011. [en línia]. [Consulta: 16 setembre 2015]. Disponible a: <https://en.wikipedia.org/wiki/Entscheidungsproblem>

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#### Halting problem

In computability theory, the halting problem is the problem of determining, from a description of an arbitrary computer program and an input, whether the program will finish running or continue to run forever.

Alan Turing proved in 1936 that a general algorithm to solve the halting problem for all possible program-input pairs cannot exist. A key part of the proof was a mathematical definition of a computer and program, which became known as a Turing machine; the halting problem is undecidable over Turing machines. It is one of the first examples of a decision problem.

Jack Copeland (2004) attributes the term halting problem to Martin Davis.

Citació: "Halting problem" A: *Wikipedia*. Wikimedia Foundation, 2011. [en línia]. [Consulta: 16 setembre 2015]. Disponible a: <https://en.wikipedia.org/wiki/Halting_problem>

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#### Mathematical biology or Biomathematics

Mathematical and theoretical biology is an interdisciplinary scientific research field with a range of applications in biology, biotechnology, and medicine. The field may be referred to as mathematical biology or biomathematics to stress the mathematical side, or as theoretical biology to stress the biological side. Mathematical biology aims at the mathematical representation, treatment and modeling of biological processes, using a variety of applied mathematical techniques and tools. It has both theoretical and practical applications in biological, biomedical and biotechnology research. For example, in cell biology, protein interactions are often represented as "cartoon" models, which, although easy to visualize, do not accurately describe the systems studied. In order to do this, precise mathematical models are required. By describing the systems in a quantitative manner, their behavior can be better simulated, and hence properties can be predicted that might not be evident to the experimenter.

Such mathematical areas as calculus, probability theory, statistics, linear algebra, abstract algebra, graph theory, combinatorics, algebraic geometry, topology, dynamical systems, differential equations and coding theory are now being applied in biology. Some mathematical areas, such as certain methodologies in statistics, were developed as tools during the conduct of research into mathematical biology.

Citació: "Mathematical biology" A: *Wikipedia*. Wikimedia Foundation, 2011. [en línia]. [Consulta: 16 setembre 2015]. Disponible a: <https://en.wikipedia.org/wiki/Mathematical_and_theoretical_biology>

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#### Mathematical logic

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.

Citació: "Mathematical logic" A: *Wikipedia*. Wikimedia Foundation, 2011. [en línia]. [Consulta: 16 setembre 2015]. Disponible a: <https://en.wikipedia.org/wiki/Mathematical_logic>

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#### Morphogenesis

Morphogenesis (from the Greek morphê shape and genesis creation, literally, "beginning of the shape") is the biological process that causes an organism to develop its shape. It is one of three fundamental aspects of developmental biology along with the control of cell growth and cellular differentiation.

The process controls the organized spatial distribution of cells during the embryonic development of an organism. Morphogenesis can take place also in a mature organism, in cell culture or inside tumor cell masses. Morphogenesis also describes the development of unicellular life forms that do not have an embryonic stage in their life cycle, or describes the evolution of a body structure within a taxonomic group.

Morphogenetic responses may be induced in organisms by hormones, by environmental chemicals ranging from substances produced by other organisms to toxic chemicals or radionuclides released as pollutants, and other plants, or by mechanical stresses induced by spatial patterning of the cells.

Citació: "Morphogenesis" A: *Wikipedia*. Wikimedia Foundation, 2011. [en línia]. [Consulta: 16 setembre 2015]. Disponible a: <https://en.wikipedia.org/wiki/Morphogenesis>

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#### Recursion

Recursion is the process of repeating items in a self-similar way. For instance, when the surfaces of two mirrors are exactly parallel with each other, the nested images that occur are a form of infinite recursion. The term has a variety of meanings specific to a variety of disciplines ranging from linguistics to logic. The most common application of recursion is in mathematics and computer science, in which it refers to a method of defining functions in which the function being defined is applied within its own definition. Specifically, this defines an infinite number of instances (function values), using a finite expression that for some instances may refer to other instances, but in such a way that no loop or infinite chain of references can occur. The term is also used more generally to describe a process of repeating objects in a self-similar way.

Citació: "Recursion" A: *Wikipedia*. Wikimedia Foundation, 2011. [en línia]. [Consulta: 16 setembre 2015]. Disponible a:

<https://en.wikipedia.org/wiki/Recursion>

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#### Turing machine

A Turing machine is an abstract "machine" that manipulates symbols on a strip of tape according to a table of rules; to be more exact, it is a mathematical model that defines such a device. Despite its simplicity, a Turing machine can simulate the logic of any computer algorithm.

The machine operates on an infinite memory tape divided into cells. The machine positions its head over a cell and "reads" (scans) the symbol there. Then per the symbol and its present place in a finite table of user-specified instructions the machine (i) writes a symbol (e.g. a digit or a letter from a finite alphabet) in the cell (some models allowing symbol erasure and/or no writing), then (ii) either moves the tape one cell left or right (some models allow no motion, some models move the head), then (iii) (as determined by the observed symbol and the machine's place in the table) either proceeds to a subsequent instruction or halts the computation.

Citació: "Turing machine" A: *Wikipedia*. Wikimedia Foundation, 2011. [en línia]. [Consulta: 16 setembre 2015]. Disponible a: <https://en.wikipedia.org/wiki/Turing_machine>

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#### Turing test

The Turing test is a test of a machine's ability to exhibit intelligent behavior equivalent to, or indistinguishable from, that of a human. Alan Turing proposed that a human evaluator would judge natural language conversations between a human and a machine that is designed to generate human-like responses. The evaluator would be aware that one of the two partners in conversation is a machine, and all participants would be separated from one another. The conversation would be limited to a text-only channel such as a computer keyboard and screen so that the result would not be dependent on the machine's ability to render words as speech. If the evaluator cannot reliably tell the machine from the human (Turing originally suggested that the machine would convince a human 70% of the time after five minutes of conversation), the machine is said to have passed the test. The test does not check the ability to give correct answers to questions, only how closely answers resemble those a human would give.

Citació: "Turing test" A: *Wikipedia*. Wikimedia Foundation, 2011. [en línia]. [Consulta: 16 setembre 2015]. Disponible a:

<https://en.wikipedia.org/wiki/Turing_test>

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