Turing machineA 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.
Universal Turing machineIn computer science, a universal Turing machine (UTM) is a Turing machine capable of computing any computable sequence, as described by Alan Turing in his seminal paper "On Computable Numbers, with an Application to the Entscheidungsproblem". Common sense might say that a universal machine is impossible, but Turing proves that it is possible. He suggested that we may compare a man in the process of computing a real number to a machine which is only capable of a finite number of conditions q 1: q 2 . ....
Automata theoryAutomata theory is the study of abstract machines and automata, as well as the computational problems that can be solved using them. It is a theory in theoretical computer science. The word automata comes from the Greek word αὐτόματος, which means "self-acting, self-willed, self-moving". An automaton (automata in plural) is an abstract self-propelled computing device which follows a predetermined sequence of operations automatically. An automaton with a finite number of states is called a Finite Automaton (FA) or Finite-State Machine (FSM).
Nondeterministic Turing machineIn theoretical computer science, a nondeterministic Turing machine (NTM) is a theoretical model of computation whose governing rules specify more than one possible action when in some given situations. That is, an NTM's next state is not completely determined by its action and the current symbol it sees, unlike a deterministic Turing machine. NTMs are sometimes used in thought experiments to examine the abilities and limits of computers.
Theory of computationIn theoretical computer science and mathematics, the theory of computation is the branch that deals with what problems can be solved on a model of computation, using an algorithm, how efficiently they can be solved or to what degree (e.g., approximate solutions versus precise ones). The field is divided into three major branches: automata theory and formal languages, computability theory, and computational complexity theory, which are linked by the question: "What are the fundamental capabilities and limitations of computers?".
Decider (Turing machine)In computability theory, a decider is a Turing machine that halts for every input. A decider is also called a total Turing machine as it represents a total function. Because it always halts, such a machine is able to decide whether a given string is a member of a formal language. The class of languages which can be decided by such machines is the set of recursive languages. Given an arbitrary Turing machine, determining whether it is a decider is an undecidable problem.
Cellular automatonA 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 states, such as on and off (in contrast to a coupled map lattice).
Probabilistic Turing machineIn theoretical computer science, a probabilistic Turing machine is a non-deterministic Turing machine that chooses between the available transitions at each point according to some probability distribution. As a consequence, a probabilistic Turing machine can—unlike a deterministic Turing Machine—have stochastic results; that is, on a given input and instruction state machine, it may have different run times, or it may not halt at all; furthermore, it may accept an input in one execution and reject the same input in another execution.
Turing completenessIn 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 decide other data-manipulation rule sets. Turing completeness is used as a way to express the power of such a data-manipulation rule set.
Reel-to-reel audio tape recordingReel-to-reel audio tape recording, also called open-reel recording, is magnetic tape audio recording in which the recording tape is spooled between reels. To prepare for use, the supply reel (or feed reel) containing the tape is placed on a spindle or hub. The end of the tape is manually pulled from the reel, threaded through mechanical guides and over a tape head assembly, and attached by friction to the hub of the second, initially empty takeup reel. Reel-to-reel systems use tape that is wide, which normally moves at .
Oracle machineIn complexity theory and computability theory, an oracle machine is an abstract machine used to study decision problems. It can be visualized as a Turing machine with a black box, called an oracle, which is able to solve certain problems in a single operation. The problem can be of any complexity class. Even undecidable problems, such as the halting problem, can be used. An oracle machine can be conceived as a Turing machine connected to an oracle.
Electroacoustic musicElectroacoustic music is a genre of popular and Western art music in which composers use technology to manipulate the timbres of acoustic sounds, sometimes by using audio signal processing, such as reverb or harmonizing, on acoustical instruments. It originated around the middle of the 20th century, following the incorporation of electric sound production into compositional practice.
Transition systemIn theoretical computer science, a transition system is a concept used in the study of computation. It is used to describe the potential behavior of discrete systems. It consists of states and transitions between states, which may be labeled with labels chosen from a set; the same label may appear on more than one transition. If the label set is a singleton, the system is essentially unlabeled, and a simpler definition that omits the labels is possible.
Musique concrèteMusique concrète (myzik kɔ̃kʁɛt; concrete music) is a type of music composition that utilizes recorded sounds as raw material. Sounds are often modified through the application of audio signal processing and tape music techniques, and may be assembled into a form of sound collage. It can feature sounds derived from recordings of musical instruments, the human voice, and the natural environment as well as those created using sound synthesis and computer-based digital signal processing.
Non-analytic smooth functionIn mathematics, smooth functions (also called infinitely differentiable functions) and analytic functions are two very important types of functions. One can easily prove that any analytic function of a real argument is smooth. The converse is not true, as demonstrated with the counterexample below. One of the most important applications of smooth functions with compact support is the construction of so-called mollifiers, which are important in theories of generalized functions, such as Laurent Schwartz's theory of distributions.
Bump functionIn mathematics, a bump function (also called a test function) is a function on a Euclidean space which is both smooth (in the sense of having continuous derivatives of all orders) and compactly supported. The set of all bump functions with domain forms a vector space, denoted or The dual space of this space endowed with a suitable topology is the space of distributions. The function given by is an example of a bump function in one dimension.
Finite-state transducerA finite-state transducer (FST) is a finite-state machine with two memory tapes, following the terminology for Turing machines: an input tape and an output tape. This contrasts with an ordinary finite-state automaton, which has a single tape. An FST is a type of finite-state automaton (FSA) that maps between two sets of symbols. An FST is more general than an FSA. An FSA defines a formal language by defining a set of accepted strings, while an FST defines relations between sets of strings.
AlphabetAn alphabet is a standardized set of basic written graphemes (called letters) representing phonemes, units of sounds that distinguish words, of certain spoken languages. Not all writing systems represent language in this way; in a syllabary, each character represents a syllable, and logographic systems use characters to represent words, morphemes, or other semantic units. The Egyptians have created the first alphabet in a technical sense.
ColorColor (American English) or colour (Commonwealth English) is the visual perception based on the electromagnetic spectrum. Though color is not an inherent property of matter, color perception is related to an object's light absorption, reflection, emission spectra and interference. For most humans, color are perceived in the visible light spectrum with three types of cone cells (trichromacy). Other animals may have a different number of cone cell types or have eyes sensitive to different wavelength, such as bees that can distinguish ultraviolet, and thus have a different color sensitivity range.
Latin alphabetThe Latin alphabet, also known as the Roman alphabet, is the collection of letters originally used by the ancient Romans to write the Latin language. Largely unaltered with the exception of extensions (such as diacritics), it forms the Latin script that is used to write many modern European languages, including English. With modifications, it is also used for other alphabets, such as the Vietnamese alphabet. Its modern repertoire is standardised as the ISO basic Latin alphabet.
