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Computer
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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, such computers are used as control systems for a very wide variety of industrial and consumer devices. The Internet is run on computers and it millions of other computers. Since ancient times, simple manual devices like the abacus aided people in doing calculations, early in the Industrial Revolution, some mechanical devices were built to automate long tedious tasks, such as guiding patterns for looms. More sophisticated electrical machines did specialized analog calculations in the early 20th century, the first digital electronic calculating machines were developed during World War II. The speed, power, and versatility of computers has increased continuously and dramatically since then, conventionally, a modern computer consists of at least one processing element, typically a central processing unit, and some form of memory. The processing element carries out arithmetic and logical operations, and a sequencing, peripheral devices include input devices, output devices, and input/output devices that perform both functions. Peripheral devices allow information to be retrieved from an external source and this usage of the term referred to a person who carried out calculations or computations. The word continued with the same meaning until the middle of the 20th century, from the end of the 19th century the word began to take on its more familiar meaning, a machine that carries out computations. The Online Etymology Dictionary gives the first attested use of computer in the 1640s, one who calculates, the Online Etymology Dictionary states that the use of the term to mean calculating machine is from 1897. The Online Etymology Dictionary indicates that the use of the term. 1945 under this name, theoretical from 1937, as Turing machine, devices have been used to aid computation for thousands of years, mostly using one-to-one correspondence with fingers. The earliest counting device was probably a form of tally stick, later record keeping aids throughout the Fertile Crescent included calculi which represented counts of items, probably livestock or grains, sealed in hollow unbaked clay containers. The use of counting rods is one example, the abacus was initially used for arithmetic tasks. The Roman abacus was developed from used in Babylonia as early as 2400 BC. Since then, many forms of reckoning boards or tables have been invented. In a medieval European counting house, a checkered cloth would be placed on a table, the Antikythera mechanism is believed to be the earliest mechanical analog computer, according to Derek J. de Solla Price. It was designed to calculate astronomical positions and it was discovered in 1901 in the Antikythera wreck off the Greek island of Antikythera, between Kythera and Crete, and has been dated to circa 100 BC
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Computer science
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Computer science is the study of the theory, experimentation, and engineering that form the basis for the design and use of computers. An alternate, more succinct definition of 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 and its fields can be divided into a variety of theoretical and practical disciplines. Some fields, such as computational complexity theory, are highly abstract, other fields still focus on challenges in implementing computation. Human–computer interaction considers the challenges in making computers and computations useful, usable, the earliest foundations of what would become computer science predate the invention of the modern digital computer. Machines for calculating fixed numerical tasks such as the abacus have existed since antiquity, further, algorithms for performing computations have existed since antiquity, even before the development of sophisticated computing equipment. Wilhelm Schickard designed and constructed the first working mechanical calculator in 1623, in 1673, Gottfried Leibniz demonstrated a digital mechanical calculator, called the Stepped Reckoner. He may be considered the first computer scientist and information theorist, for, among other reasons and he started developing this machine in 1834, and in less than two years, he had sketched out many of the salient features of the modern computer. A crucial step was the adoption of a card system derived from the Jacquard loom making it infinitely programmable. Around 1885, Herman Hollerith invented the tabulator, which used punched cards to process statistical information, when the machine was finished, some hailed it as Babbages dream come true. During the 1940s, as new and more powerful computing machines were developed, as it became clear that computers could be used for more than just mathematical calculations, the field of computer science broadened to study computation in general. Computer science began to be established as an academic discipline in the 1950s. The worlds first computer science program, the Cambridge Diploma in Computer Science. The first computer science program in the United States was formed at Purdue University in 1962. Since practical computers became available, many applications of computing have become distinct areas of study in their own rights and it is the now well-known IBM brand that formed part of the computer science revolution during this time. IBM released the IBM704 and later the IBM709 computers, still, working with the IBM was frustrating if you had misplaced as much as one letter in one instruction, the program would crash, and you would have to start the whole process over again. During the late 1950s, the science discipline was very much in its developmental stages. Time has seen significant improvements in the usability and effectiveness of computing technology, modern society has seen a significant shift in the users of computer technology, from usage only by experts and professionals, to a near-ubiquitous user base
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Thought experiment
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A thought experiment considers some hypothesis, theory, or principle for the purpose of thinking through its consequences. Given the structure of the experiment, it may not be possible to perform it, perhaps the key experiment in the history of modern science is Galileos demonstration that falling objects must fall at the same rate regardless of their masses. The experiment is described by Galileo in Discorsi e dimostrazioni matematiche thus, do you not agree with me in this opinion. Hence the heavier body moves with less speed than the lighter, thus you see how, from your assumption that the heavier body moves more rapidly than the lighter one, I infer that the heavier body moves more slowly. Although the extract does not convey the elegance and power of the demonstration terribly well, it is clear that it is a thought experiment, instead, many philosophers prefer to consider Thought Experiments to be merely the use of a hypothetical scenario to help understand the way things are. Thought experiments have used in a variety of fields, including philosophy, law, physics. In philosophy, they have used at least since classical antiquity. In law, they were well-known to Roman lawyers quoted in the Digest, in physics and other sciences, notable thought experiments date from the 19th and especially the 20th century, but examples can be found at least as early as Galileo. Johann Witt-Hansen established that Hans Christian Ørsted was the first to use the Latin-German mixed term Gedankenexperiment circa 1812, Ørsted was also the first to use its entirely German equivalent, Gedankenversuch, in 1820. The English term thought experiment was coined from Machs Gedankenexperiment, prior to its emergence, the activity of posing hypothetical questions that employed subjunctive reasoning had existed for a very long time. However, people had no way of categorizing it or speaking about it and this helps to explain the extremely wide and diverse range of the application of the term thought experiment once it had been introduced into English. In physics and other sciences many thought experiments date from the 19th and especially the 20th Century, in Galileo’s thought experiment, for example, the rearrangement of empirical experience consists in the original idea of combining bodies of different weight. Thought experiments have used in philosophy, physics, and other fields. In law, the hypothetical is frequently used for such experiments. Regardless of their goal, all thought experiments display a patterned way of thinking that is designed to allow us to explain, predict and control events in a better. However, they may make those theories themselves irrelevant, and could create new problems that are just as difficult. Ensure the avoidance of past failures Scientists tend to use thought experiments as imaginary, in these cases, the result of the proxy experiment will often be so clear that there will be no need to conduct a physical experiment at all. Scientists also use thought experiments when particular physical experiments are impossible to conduct, such as Einsteins thought experiment of chasing a light beam, leading to Special Relativity
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Turing machine
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Despite the models simplicity, given any computer algorithm, a Turing machine can be constructed that is capable of simulating that algorithms logic. The machine operates on an infinite memory tape divided into discrete cells, the machine positions its head over a cell and reads the symbol there. The Turing machine was invented in 1936 by Alan Turing, who called it an a-machine, thus, Turing machines prove fundamental limitations on the power of mechanical computation. Turing completeness is the ability for a system of instructions to simulate a Turing machine, a Turing machine is a general example of a CPU that controls all data manipulation done by a computer, with the canonical machine using sequential memory to store data. More specifically, it is a capable of enumerating some arbitrary subset of valid strings of an alphabet. Assuming a black box, the Turing machine cannot know whether it will eventually enumerate any one specific string of the subset with a given program and this is due to the fact that the halting problem is unsolvable, which has major implications for the theoretical limits of computing. The Turing machine is capable of processing an unrestricted grammar, which implies that it is capable of robustly evaluating first-order logic in an infinite number of ways. This is famously demonstrated through lambda calculus, a Turing machine that is able to simulate any other Turing machine is called a universal Turing machine. The thesis states that Turing machines indeed capture the notion of effective methods in logic and mathematics. Studying their abstract properties yields many insights into computer science and complexity theory, at any moment there is one symbol in the machine, it is called the scanned symbol. The machine can alter the scanned symbol, and its behavior is in part determined by that symbol, however, the tape can be moved back and forth through the machine, this being one of the elementary operations of the machine. Any symbol on the tape may therefore eventually have an innings, the Turing machine mathematically models a machine that mechanically operates on a tape. On this tape are symbols, which the machine can read and write, one at a time, in the original article, Turing imagines not a mechanism, but a person whom he calls the computer, who executes these deterministic mechanical rules slavishly. If δ is not defined on the current state and the current tape symbol, Q0 ∈ Q is the initial state F ⊆ Q is the set of final or accepting states. The initial tape contents is said to be accepted by M if it eventually halts in a state from F, Anything that operates according to these specifications is a Turing machine. The 7-tuple for the 3-state busy beaver looks like this, Q = Γ = b =0 Σ = q 0 = A F = δ = see state-table below Initially all tape cells are marked with 0. In the words of van Emde Boas, p.6, The set-theoretical object provides only partial information on how the machine will behave and what its computations will look like. For instance, There will need to be many decisions on what the symbols actually look like, and a failproof way of reading and writing symbols indefinitely
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Microprocessor
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A microprocessor is a computer processor which incorporates the functions of a computers central processing unit on a single integrated circuit, or at most a few integrated circuits. Microprocessors contain both combinational logic and sequential digital logic, Microprocessors operate on numbers and symbols represented in the binary numeral system. The integration of a whole CPU onto a chip or on a few chips greatly reduced the cost of processing power. Integrated circuit processors are produced in numbers by highly automated processes resulting in a low per unit cost. Single-chip processors increase reliability as there are many electrical connections to fail. As microprocessor designs get better, the cost of manufacturing a chip generally stays the same, before microprocessors, small computers had been built using racks of circuit boards with many medium- and small-scale integrated circuits. Microprocessors combined this into one or a few large-scale ICs, the internal arrangement of a microprocessor varies depending on the age of the design and the intended purposes of the microprocessor. Advancing technology makes more complex and powerful chips feasible to manufacture, a minimal hypothetical microprocessor might only include an arithmetic logic unit and a control logic section. The ALU performs operations such as addition, subtraction, and operations such as AND or OR, each operation of the ALU sets one or more flags in a status register, which indicate the results of the last operation. The control logic retrieves instruction codes from memory and initiates the sequence of operations required for the ALU to carry out the instruction, a single operation code might affect many individual data paths, registers, and other elements of the processor. As integrated circuit technology advanced, it was feasible to manufacture more and more complex processors on a single chip, the size of data objects became larger, allowing more transistors on a chip allowed word sizes to increase from 4- and 8-bit words up to todays 64-bit words. Additional features were added to the architecture, more on-chip registers sped up programs. Floating-point arithmetic, for example, was not available on 8-bit microprocessors. Integration of the point unit first as a separate integrated circuit and then as part of the same microprocessor chip. Occasionally, physical limitations of integrated circuits made such practices as a bit slice approach necessary, instead of processing all of a long word on one integrated circuit, multiple circuits in parallel processed subsets of each data word. With the ability to put large numbers of transistors on one chip and this CPU cache has the advantage of faster access than off-chip memory, and increases the processing speed of the system for many applications. Processor clock frequency has increased more rapidly than external memory speed, except in the recent past, a microprocessor is a general purpose system. Several specialized processing devices have followed from the technology, A digital signal processor is specialized for signal processing, graphics processing units are processors designed primarily for realtime rendering of 3D images
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Algorithm
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In mathematics and computer science, an algorithm is a self-contained sequence of actions to be performed. Algorithms can perform calculation, data processing and automated reasoning tasks, an algorithm is an effective method that can be expressed within a finite amount of space and time and in a well-defined formal language for calculating a function. The transition from one state to the next is not necessarily deterministic, some algorithms, known as randomized algorithms, giving a formal definition of algorithms, corresponding to the intuitive notion, remains a challenging problem. In English, it was first used in about 1230 and then by Chaucer in 1391, English adopted the French term, but it wasnt until the late 19th century that algorithm took on the meaning that it has in modern English. Another early use of the word is from 1240, in a manual titled Carmen de Algorismo composed by Alexandre de Villedieu and it begins thus, Haec algorismus ars praesens dicitur, in qua / Talibus Indorum fruimur bis quinque figuris. Which translates as, Algorism is the art by which at present we use those Indian figures, the poem is a few hundred lines long and summarizes the art of calculating with the new style of Indian dice, or Talibus Indorum, or Hindu numerals. An informal definition could be a set of rules that precisely defines a sequence of operations, which would include all computer programs, including programs that do not perform numeric calculations. Generally, a program is only an algorithm if it stops eventually, but humans can do something equally useful, in the case of certain enumerably infinite sets, They can give explicit instructions for determining the nth member of the set, for arbitrary finite n. An enumerably infinite set is one whose elements can be put into one-to-one correspondence with the integers, the concept of algorithm is also used to define the notion of decidability. That notion is central for explaining how formal systems come into being starting from a set of axioms. In logic, the time that an algorithm requires to complete cannot be measured, from such uncertainties, that characterize ongoing work, stems the unavailability of a definition of algorithm that suits both concrete and abstract usage of the term. Algorithms are essential to the way computers process data, thus, an algorithm can be considered to be any sequence of operations that can be simulated by a Turing-complete system. Although this may seem extreme, the arguments, in its favor are hard to refute. Gurevich. Turings informal argument in favor of his thesis justifies a stronger thesis, according to Savage, an algorithm is a computational process defined by a Turing machine. Typically, when an algorithm is associated with processing information, data can be read from a source, written to an output device. Stored data are regarded as part of the state of the entity performing the algorithm. In practice, the state is stored in one or more data structures, for some such computational process, the algorithm must be rigorously defined, specified in the way it applies in all possible circumstances that could arise. That is, any conditional steps must be dealt with, case-by-case
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Finite-state machine
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A finite-state machine or finite-state automaton, finite automaton, or simply a state machine, is a mathematical model of computation. It is a machine that can be in exactly one of a finite number of states at any given time. The FSM can change from one state to another in response to external inputs. A FSM is defined by a list of its states, its state. The behavior of machines can be observed in many devices in modern society that perform a predetermined sequence of actions depending on a sequence of events with which they are presented. The finite state machine has less power than some other models of computation such as the Turing machine. The computational power distinction means there are tasks that a Turing machine can do. This is because a FSMs memory is limited by the number of states it has, FSMs are studied in the more general field of automata theory. An example of a mechanism that can be modeled by a machine is a turnstile. A turnstile, used to access to subways and amusement park rides, is a gate with three rotating arms at waist height, one across the entryway. Initially the arms are locked, blocking the entry, preventing patrons from passing through, depositing a coin or token in a slot on the turnstile unlocks the arms, allowing a single customer to push through. After the customer passes through, the arms are locked again until another coin is inserted, considered as a state machine, the turnstile has two possible states, Locked and Unlocked. There are two inputs that affect its state, putting a coin in the slot and pushing the arm. In the locked state, pushing on the arm has no effect, no matter how many times the input push is given, putting a coin in – that is, giving the machine a coin input – shifts the state from Locked to Unlocked. In the unlocked state, putting additional coins in has no effect, however, a customer pushing through the arms, giving a push input, shifts the state back to Locked. Each state is represented by a node, edges show the transitions from one state to another. Each arrow is labeled with the input that triggers that transition, an input that doesnt cause a change of state is represented by a circular arrow returning to the original state. The arrow into the Locked node from the dot indicates it is the initial state
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Computer engineering
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Computer engineering is a discipline that integrates several fields of electrical engineering and computer science required to develop computer hardware and software. Computer engineers usually have training in engineering, software design. This field of engineering not only focuses on how computer systems themselves work, Computer engineers are also suited for robotics research, which relies heavily on using digital systems to control and monitor electrical systems like motors, communications, and sensors. Other institutions may require engineering students to one or two years of General Engineering before declaring computer engineering as their primary focus. The first computer engineering program in the United States was established at Case Western Reserve University in 1972. As of 2015, there were 238 ABET-accredited computer engineering programs in the US, in Europe, accreditation of computer engineering schools is done by a variety of agencies part of the EQANIE network. Both computer engineering and electronic engineering programs include analog and digital circuit design in their curriculum, as with most engineering disciplines, having a sound knowledge of mathematics and science is necessary for computer engineers. There are two major specialties in computer engineering, software and hardware, Computer software engineers develop, design, and test software. They construct, and maintain computer programs, as well as set up such as intranets for companies. Software engineers can design or code new applications to meet the needs of a business or individual. Some software engineers work independently as freelancers and sell their software products/applications to an enterprise or individual, most computer hardware engineers research, develop, design, and test various computer equipment. This can range from circuit boards and microprocessors to routers, some update existing computer equipment to be more efficient and work with newer software. Most computer hardware engineers work in laboratories and high-tech manufacturing firms. Some also work for the federal government, according to BLS, 95% of computer hardware engineers work in metropolitan areas. Approximately 33% of their work more than 40 hours a week. The median salary for employed qualified computer hardware engineers was $100,920 per year or $48.52 per hour, Computer hardware engineers held 83,300 jobs in 2012 in the USA. There are many specialty areas in the field of computer engineering, examples include work on wireless communications, multi-antenna systems, optical transmission, and digital watermarking. Those focusing on communications and wireless networks, work advancements in telecommunications systems and networks, modulation and error-control coding, high-speed network design, interference suppression and modulation, design and analysis of fault-tolerant system, and storage and transmission schemes are all a part of this specialty
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Computational complexity theory
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A problem is regarded as inherently difficult if its solution requires significant resources, whatever the algorithm used. The theory formalizes this intuition, by introducing mathematical models of computation to study these problems and quantifying the amount of resources needed to solve them, such as time and storage. Other complexity measures are used, such as the amount of communication, the number of gates in a circuit. One of the roles of computational complexity theory is to determine the limits on what computers can. Closely related fields in computer science are analysis of algorithms. More precisely, computational complexity theory tries to classify problems that can or cannot be solved with appropriately restricted resources, a computational problem can be viewed as an infinite collection of instances together with a solution for every instance. The input string for a problem is referred to as a problem instance. In computational complexity theory, a problem refers to the question to be solved. In contrast, an instance of this problem is a rather concrete utterance, for example, consider the problem of primality testing. The instance is a number and the solution is yes if the number is prime, stated another way, the instance is a particular input to the problem, and the solution is the output corresponding to the given input. For this reason, complexity theory addresses computational problems and not particular problem instances, when considering computational problems, a problem instance is a string over an alphabet. Usually, the alphabet is taken to be the binary alphabet, as in a real-world computer, mathematical objects other than bitstrings must be suitably encoded. For example, integers can be represented in binary notation, and graphs can be encoded directly via their adjacency matrices and this can be achieved by ensuring that different representations can be transformed into each other efficiently. Decision problems are one of the objects of study in computational complexity theory. A decision problem is a type of computational problem whose answer is either yes or no. A decision problem can be viewed as a language, where the members of the language are instances whose output is yes. The objective is to decide, with the aid of an algorithm, if the algorithm deciding this problem returns the answer yes, the algorithm is said to accept the input string, otherwise it is said to reject the input. An example of a problem is the following
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Theory of computation
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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. In order to perform a study of computation, computer scientists work with a mathematical abstraction of computers called a model of computation. There are several models in use, but the most commonly examined is the Turing machine and it might seem that the potentially infinite memory capacity is an unrealizable attribute, but any decidable problem solved by a Turing machine will always require only a finite amount of memory. So in principle, any problem that can be solved by a Turing machine can be solved by a computer that has an amount of memory. The theory of computation can be considered the creation of models of all kinds in the field of computer science, therefore, mathematics and logic are used. In the last century it became an independent academic discipline and was separated from mathematics, some pioneers of the theory of computation were Alonzo Church, Kurt Gödel, Alan Turing, Stephen Kleene, John von Neumann and Claude Shannon. Automata theory is the study of abstract machines and the problems that can be solved using these machines. These abstract machines are called automata, Automata comes from the Greek word which means that something is doing something by itself. Automata theory is closely related to formal language theory, as the automata are often classified by the class of formal languages they are able to recognize. An automaton can be a representation of a formal language that may be an infinite set. Automata are used as models for computing machines, and are used for proofs about computability. Language theory is a branch of mathematics concerned with describing languages as a set of operations over an alphabet and it is closely linked with automata theory, as automata are used to generate and recognize formal languages. Because automata are used as models for computation, formal languages are the mode of specification for any problem that must be computed. Computability theory deals primarily with the question of the extent to which a problem is solvable on a computer, much of computability theory builds on the halting problem result. Many mathematicians and computational theorists who study recursion theory will refer to it as computability theory, Complexity theory considers not only whether a problem can be solved at all on a computer, but also how efficiently the problem can be solved. In order to analyze how much time and space a given algorithm requires, for example, finding a particular number in a long list of numbers becomes harder as the list of numbers grows larger. If we say there are n numbers in the list, then if the list is not sorted or indexed in any way we may have to look at every number in order to find the number were seeking. We thus say that in order to solve this problem, the needs to perform a number of steps that grows linearly in the size of the problem
