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Turing-complete
In computability theory, a system of data-manipulation rules (such as a model of computation, a computer's instruction set, a programming language, or a cellular automaton) is said to be Turing-complete or computationally universal if it can be used to simulate any Turing machine (devised by English mathematician and computer scientist Alan Turing). This means that this system is able to recognize or decode other data-manipulation rule sets. Turing completeness is used as a way to express the power of such a data-manipulation rule set. Virtually all programming languages today are Turing-complete. A related concept is that of Turing equivalence two computers P and Q are called equivalent if P can simulate Q and Q can simulate P. The Church–Turing thesis conjectures that any function whose values can be computed by an algorithm can be computed by a Turing machine, and therefore that if any real-world computer can simulate a Turing machine, it is Turing equivalent to a Turing ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer
A computer is a machine that can be Computer programming, programmed to automatically Execution (computing), carry out sequences of arithmetic or logical operations (''computation''). Modern digital electronic computers can perform generic sets of operations known as Computer program, ''programs'', which enable computers to perform a wide range of tasks. The term computer system may refer to a nominally complete computer that includes the Computer hardware, hardware, operating system, software, and peripheral equipment needed and used for full operation; or to a group of computers that are linked and function together, such as a computer network or computer cluster. A broad range of Programmable logic controller, industrial and Consumer electronics, consumer products use computers as control systems, including simple special-purpose devices like microwave ovens and remote controls, and factory devices like industrial robots. Computers are at the core of general-purpose devices ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
ENIAC
ENIAC (; Electronic Numerical Integrator and Computer) was the first Computer programming, programmable, Electronics, electronic, general-purpose digital computer, completed in 1945. Other computers had some of these features, but ENIAC was the first to have them all. It was Turing-complete and able to solve "a large class of numerical problems" through reprogramming. ENIAC was designed by John Mauchly and J. Presper Eckert to calculate artillery external ballistics, firing tables for the United States Army's Ballistic Research Laboratory (which later became a part of the United States Army Research Laboratory, Army Research Laboratory). However, its first program was a study of the feasibility of the thermonuclear weapon. ENIAC was completed in 1945 and first put to work for practical purposes on December 10, 1945.* ENIAC was formally dedicated at the University of Pennsylvania on February 15, 1946, having cost $487,000 (), and called a "Giant Brain" by the press. It had ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cellular Automaton
A cellular automaton (pl. cellular automata, abbrev. CA) is a discrete model of computation studied in automata theory. Cellular automata are also called cellular spaces, tessellation automata, homogeneous structures, cellular structures, tessellation structures, and iterative arrays. Cellular automata have found application in various areas, including physics, theoretical biology and microstructure modeling. A cellular automaton consists of a regular grid of ''cells'', each in one of a finite number of ''State (computer science), states'', such as ''on'' and ''off'' (in contrast to a coupled map lattice). The grid can be in any finite number of dimensions. For each cell, a set of cells called its ''neighborhood'' is defined relative to the specified cell. An initial state (time ''t'' = 0) is selected by assigning a state for each cell. A new ''generation'' is created (advancing ''t'' by 1), according to some fixed ''rule'' (generally, a mathematical function) that dete ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Z3 (computer)
The Z3 was a German electromechanical computer designed by Konrad Zuse in 1938, and completed in 1941. It was the world's first working Computer programming, programmable, fully automatic digital computer. The Z3 was built with 2,600 relays, implementing a 22-bit Word (data type), word length that operated at a clock frequency of about 5–10 Hertz, Hz. Program code was stored on punched celluloid, film. Initial values were entered manually. The Z3 was completed in Berlin in 1941. It was not considered vital, so it was never put into everyday operation. Based on the work of the German aerodynamics engineer Hans Georg Küssner (known for the Küssner effect), a "Program to Compute a Complex Matrix" was written and used to solve wing flutter problems. Zuse asked the German government for funding to replace the relays with fully electronic switches, but funding was denied during World War II since such development was deemed "not war-important". The original Z3 was destroyed ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Konrad Zuse
Konrad Ernst Otto Zuse (; ; 22 June 1910 – 18 December 1995) was a German civil engineer, List of pioneers in computer science, pioneering computer scientist, inventor and businessman. His greatest achievement was the world's first programmable computer; the functional program-controlled Turing completeness, Turing-complete Z3 (computer), Z3 became operational in May 1941. Thanks to this machine and its predecessors, Zuse is regarded by some as the inventor and father of the modern computer. Zuse was noted for the S2 computing machine, considered the first process control computer. In 1941, he founded one of the earliest computer businesses, producing the Z4 (computer), Z4, which became the world's first commercial computer. From 1943 to 1945 he designed Plankalkül, the first high-level programming language. In 1969, Zuse suggested the concept of a digital physics, computation-based universe in his book (''Calculating Space''). Much of his early work was financed by his f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Primitive Recursive Function
In computability theory, a primitive recursive function is, roughly speaking, a function that can be computed by a computer program whose loops are all "for" loops (that is, an upper bound of the number of iterations of every loop is fixed before entering the loop). Primitive recursive functions form a strict subset of those general recursive functions that are also total functions. The importance of primitive recursive functions lies in the fact that most computable functions that are studied in number theory (and more generally in mathematics) are primitive recursive. For example, addition and division, the factorial and exponential function, and the function which returns the ''n''th prime are all primitive recursive. In fact, for showing that a computable function is primitive recursive, it suffices to show that its time complexity is bounded above by a primitive recursive function of the input size. It is hence not particularly easy to devise a computable function th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computability Theory
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. The field has since expanded to include the study of generalized computability and definable set, definability. In these areas, computability theory overlaps with proof theory and effective descriptive set theory. Basic questions addressed by computability theory include: * What does it mean for a function (mathematics), function on the natural numbers to be computable? * How can noncomputable functions be classified into a hierarchy based on their level of noncomputability? Although there is considerable overlap in terms of knowledge and methods, mathematical computability theorists study the theory of relative computability, reducibility notions, and degree structures; those in the computer science field focus on the theory of computational complexity theory ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Universal Computer
A Turing machine is a mathematical model of computation describing an abstract machine that manipulates symbols on a strip of tape according to a table of rules. Despite the model's simplicity, it is capable of implementing any computer algorithm. The machine operates on an infinite memory tape divided into discrete cells, each of which can hold a single symbol drawn from a finite set of symbols called the alphabet of the machine. It has a "head" that, at any point in the machine's operation, is positioned over one of these cells, and a "state" selected from a finite set of states. At each step of its operation, the head reads the symbol in its cell. Then, based on the symbol and the machine's own present state, the machine writes a symbol into the same cell, and moves the head one step to the left or the right, or halts the computation. The choice of which replacement symbol to write, which direction to move the head, and whether to halt is based on a finite table that specif ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Programming Language
A programming language is a system of notation for writing computer programs. Programming languages are described in terms of their Syntax (programming languages), syntax (form) and semantics (computer science), semantics (meaning), usually defined by a formal language. Languages usually provide features such as a type system, Variable (computer science), variables, and mechanisms for Exception handling (programming), error handling. An Programming language implementation, implementation of a programming language is required in order to Execution (computing), execute programs, namely an Interpreter (computing), interpreter or a compiler. An interpreter directly executes the source code, while a compiler produces an executable program. Computer architecture has strongly influenced the design of programming languages, with the most common type (imperative languages—which implement operations in a specified order) developed to perform well on the popular von Neumann architecture. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Turing Machine
A Turing machine is a mathematical model of computation describing an abstract machine that manipulates symbols on a strip of tape according to a table of rules. Despite the model's simplicity, it is capable of implementing any computer algorithm. The machine operates on an infinite memory tape divided into discrete mathematics, discrete cells, each of which can hold a single symbol drawn from a finite set of symbols called the Alphabet (formal languages), alphabet of the machine. It has a "head" that, at any point in the machine's operation, is positioned over one of these cells, and a "state" selected from a finite set of states. At each step of its operation, the head reads the symbol in its cell. Then, based on the symbol and the machine's own present state, the machine writes a symbol into the same cell, and moves the head one step to the left or the right, or halts the computation. The choice of which replacement symbol to write, which direction to move the head, and whet ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algorithm
In mathematics and computer science, an algorithm () is a finite sequence of Rigour#Mathematics, mathematically rigorous instructions, typically used to solve a class of specific Computational problem, problems or to perform a computation. Algorithms are used as specifications for performing calculations and data processing. More advanced algorithms can use Conditional (computer programming), conditionals to divert the code execution through various routes (referred to as automated decision-making) and deduce valid inferences (referred to as automated reasoning). In contrast, a Heuristic (computer science), heuristic is an approach to solving problems without well-defined correct or optimal results.David A. Grossman, Ophir Frieder, ''Information Retrieval: Algorithms and Heuristics'', 2nd edition, 2004, For example, although social media recommender systems are commonly called "algorithms", they actually rely on heuristics as there is no truly "correct" recommendation. As an e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Charles Babbage
Charles Babbage (; 26 December 1791 – 18 October 1871) was an English polymath. A mathematician, philosopher, inventor and mechanical engineer, Babbage originated the concept of a digital programmable computer. Babbage is considered by some to be "List of pioneers in computer science, father of the computer". He is credited with inventing the first mechanical computer, the difference engine, that eventually led to more complex electronic designs, though all the essential ideas of modern computers are to be found in his analytical engine, programmed using a principle openly borrowed from the Jacquard loom. As part of his computer work, he also designed the first Printer (computing), computer printers. He had a broad range of interests in addition to his work on computers covered in his 1832 book ''Economy of Manufactures and Machinery''. He was an important figure in the social scene in London, and is credited with importing the "scientific soirée" from France with hi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
