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6,300 | The Brooks–Iyengar algorithm or FuseCPA Algorithm or Brooks–Iyengar hybrid algorithm is a distributed algorithm that improves both the precision and accuracy of the interval measurements taken by a distributed sensor network, even in the presence of faulty sensors. The sensor network does this by exchanging the measured value and accuracy value at every node with every other node, and computes the accuracy range and a measured value for the whole network from all of the values collected. Even if some of the data from some of the sensors is faulty, the sensor network will not malfunction | Brooks–Iyengar algorithm |
6,301 | In theoretical computer science, the busy beaver game aims at finding a terminating program of a given size that produces the most output possible. Since an endlessly looping program producing infinite output is easily conceived, such programs are excluded from the game.
More precisely, the busy beaver game consists of designing a halting Turing machine with alphabet {0,1} which writes the most 1s on the tape, using only a given set of states | Busy beaver |
6,302 | A Byzantine fault (also Byzantine generals problem, interactive consistency, source congruency, error avalanche, Byzantine agreement problem, and Byzantine failure) is a condition of a computer system, particularly distributed computing systems, where components may fail and there is imperfect information on whether a component has failed. The term takes its name from an allegory, the "Byzantine generals problem", developed to describe a situation in which, to avoid catastrophic failure of the system, the system's actors must agree on a concerted strategy, but some of these actors are unreliable.
In a Byzantine fault, a component such as a server can inconsistently appear both failed and functioning to failure-detection systems, presenting different symptoms to different observers | Byzantine fault |
6,303 | The chain rule for Kolmogorov complexity is an analogue of the chain rule for information entropy, which states:
H
(
X
,
Y
)
=
H
(
X
)
+
H
(
Y
|
X
)
{\displaystyle H(X,Y)=H(X)+H(Y|X)}
That is, the combined randomness of two sequences X and Y is the sum of the randomness of X plus whatever randomness is left in Y once we know X.
This follows immediately from the definitions of conditional and joint entropy, and the fact from probability theory that the joint probability is the product of the marginal and conditional probability:
P
(
X
,
Y
)
=
P
(
X
)
P
(
Y
|
X
)
{\displaystyle P(X,Y)=P(X)P(Y|X)}
⇒
log
P
(
X
,
Y
)
=
log
P
(
X
)
+
log
P
(
Y
|
X
)
{\displaystyle \Rightarrow \log P(X,Y)=\log P(X)+\log P(Y|X)}
The equivalent statement for Kolmogorov complexity does not hold exactly; it is true only up to a logarithmic term:
K
(
x
,
y
)
=
K
(
x
)
+
K
(
y
|
x
)
+
O
(
log
(
K
(
x
,
y
)
)
)
{\displaystyle K(x,y)=K(x)+K(y|x)+O(\log(K(x,y)))}
(An exact version, KP(x, y) = KP(x) + KP(y|x*) + O(1),
holds for the prefix complexity KP, where x* is a shortest program for x. )
It states that the shortest program printing X and Y is obtained by concatenating a shortest program printing X with a program printing Y given X, plus at most a logarithmic factor | Chain rule for Kolmogorov complexity |
6,304 | In the computer science subfield of algorithmic information theory, a Chaitin constant (Chaitin omega number) or halting probability is a real number that, informally speaking, represents the probability that a randomly constructed program will halt. These numbers are formed from a construction due to Gregory Chaitin.
Although there are infinitely many halting probabilities, one for each method of encoding programs, it is common to use the letter Ω to refer to them as if there were only one | Chaitin's constant |
6,305 | In computability theory, the Church–Turing thesis (also known as computability thesis, the Turing–Church thesis, the Church–Turing conjecture, Church's thesis, Church's conjecture, and Turing's thesis) is a thesis about the nature of computable functions. It states that a function on the natural numbers can be calculated by an effective method if and only if it is computable by a Turing machine. The thesis is named after American mathematician Alonzo Church and the British mathematician Alan Turing | Church–Turing thesis |
6,306 | In computer science and quantum physics, the Church–Turing–Deutsch principle (CTD principle) is a stronger, physical form of the Church–Turing thesis formulated by David Deutsch in 1985. The principle states that a universal computing device can simulate every physical process.
History
The principle was stated by Deutsch in 1985 with respect to finitary machines and processes | Church–Turing–Deutsch principle |
6,307 | In theoretical computer science, a circuit is a model of computation in which input values proceed through a sequence of gates, each of which computes a function. Circuits of this kind provide a generalization of Boolean circuits and a mathematical model for digital logic circuits. Circuits are defined by the gates they contain and the values the gates can produce | Circuit (computer science) |
6,308 | This is a list of computability and complexity topics, by Wikipedia page.
Computability theory is the part of the theory of computation that deals with what can be computed, in principle. Computational complexity theory deals with how hard computations are, in quantitative terms, both with upper bounds (algorithms whose complexity in the worst cases, as use of computing resources, can be estimated), and from below (proofs that no procedure to carry out some task can be very fast) | List of computability and complexity topics |
6,309 | Computable functions are the basic objects of study in computability theory. Computable functions are the formalized analogue of the intuitive notion of algorithms, in the sense that a function is computable if there exists an algorithm that can do the job of the function, i. e | Computable function |
6,310 | In mathematics, computable numbers are the real numbers that can be computed to within any desired precision by a finite, terminating algorithm. They are also known as the recursive numbers, effective numbers or the computable reals or recursive reals. The concept of a computable real number was introduced by Emile Borel in 1912, using the intuitive notion of computability available at the time | Computable number |
6,311 | In computability theory, a set of natural numbers is called computable, recursive, or decidable if there is an algorithm which takes a number as input, terminates after a finite amount of time (possibly depending on the given number) and correctly decides whether the number belongs to the set or not.
A set which is not computable is called noncomputable or undecidable.
A more general class of sets than the computable ones consists of the computably enumerable (c | Computable set |
6,312 | In computability theory, a set S of natural numbers is called computably enumerable (c. e. ), recursively enumerable (r | Computably enumerable set |
6,313 | In computer science, a computation history is a sequence of steps taken by an abstract machine in the process of computing its result. Computation histories are frequently used in proofs about the capabilities of certain machines, and particularly about the undecidability of various formal languages.
Formally, a computation history is a (normally finite) sequence of configurations of a formal automaton | Computation history |
6,314 | In computability theory, a function is called limit computable if it is the limit of a uniformly computable sequence of functions. The terms computable in the limit, limit recursive and recursively approximable are also used. One can think of limit computable functions as those admitting an eventually correct computable guessing procedure at their true value | Computation in the limit |
6,315 | Computational semiotics is an interdisciplinary field that applies, conducts, and draws on research in logic, mathematics, the theory and practice of computation, formal and natural language studies, the cognitive sciences generally, and semiotics proper. The term encompasses both the application of semiotics to computer hardware and software design and, conversely, the use of computation for performing semiotic analysis. The former focuses on what semiotics can bring to computation; the latter on what computation can bring to semiotics | Computational semiotics |
6,316 | In computability theory a cylindric numbering is a special kind of numbering first introduced by Yuri L. Ershov in 1973.
If a numbering
ν
{\displaystyle \nu }
is reducible to
μ
{\displaystyle \mu }
then there exists a computable function
f
{\displaystyle f}
with
ν
=
μ
∘
f
{\displaystyle \nu =\mu \circ f}
| Cylindric numbering |
6,317 | In computability theory a cylindrification is a construction that associates a cylindric numbering to each numbering. The concept was first introduced by Yuri L. Ershov in 1973 | Cylindrification |
6,318 | Description numbers are numbers that arise in the theory of Turing machines. They are very similar to Gödel numbers, and are also occasionally called "Gödel numbers" in the literature. Given some universal Turing machine, every Turing machine can, given its encoding on that machine, be assigned a number | Description number |
6,319 | Digital physics is a speculative idea that the universe can be conceived of as a vast, digital computation device, or as the output of a deterministic or probabilistic computer program. The hypothesis that the universe is a digital computer was proposed by Konrad Zuse in his 1969 book Rechnender Raum ("Calculating Space"). The term digital physics was coined by Edward Fredkin in 1978, who later came to prefer the term digital philosophy | Digital physics |
6,320 | In logic, mathematics and computer science, especially metalogic and computability theory, an effective method or effective procedure is a procedure for solving a problem by any intuitively 'effective' means from a specific class. An effective method is sometimes also called a mechanical method or procedure.
Definition
The definition of an effective method involves more than the method itself | Effective method |
6,321 | In mathematics and computer science, the Entscheidungsproblem (German for 'decision problem'; pronounced [ɛntˈʃaɪ̯dʊŋspʁoˌbleːm]) is a challenge posed by David Hilbert and Wilhelm Ackermann in 1928. The problem asks for an algorithm that considers, as input, a statement and answers "yes" or "no" according to whether the statement is universally valid, i. e | Entscheidungsproblem |
6,322 | An enumerator is a Turing machine with an attached printer. The Turing machine can use that printer as an output device to print strings. Every time the Turing machine wants to add a string to the list, it sends the string to the printer | Enumerator (computer science) |
6,323 | In a conventional finite state machine, the transition is associated with a set of input Boolean conditions and a set of output Boolean functions. In an extended finite state machine (EFSM) model, the transition can be expressed by an “if statement” consisting of a set of trigger conditions. If trigger conditions are all satisfied, the transition is fired, bringing the machine from the current state to the next state and performing the specified data operations | Extended finite-state machine |
6,324 | The First Draft of a Report on the EDVAC (commonly shortened to First Draft) is an incomplete 101-page document written by John von Neumann and distributed on June 30, 1945 by Herman Goldstine, security officer on the classified ENIAC project. It contains the first published description of the logical design of a computer using the stored-program concept, which has come to be known as the von Neumann architecture; the name has become controversial due to von Neumann's failure to name other contributors.
History
Von Neumann wrote the report by hand while commuting by train to Los Alamos, New Mexico and mailed the handwritten notes back to Philadelphia | First Draft of a Report on the EDVAC |
6,325 | In mathematical logic, a Gödel numbering is a function that assigns to each symbol and well-formed formula of some formal language a unique natural number, called its Gödel number. The concept was developed by Kurt Gödel for the proof of his incompleteness theorems. (Gödel 1931)
A Gödel numbering can be interpreted as an encoding in which a number is assigned to each symbol of a mathematical notation, after which a sequence of natural numbers can then represent a sequence of symbols | Gödel numbering |
6,326 | 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. The halting problem is undecidable, meaning that no general algorithm exists that solves the halting problem for all possible program–input pairs.
A key part of the formal statement of the problem is a mathematical definition of a computer and program, usually via a Turing machine | Halting problem |
6,327 | The history of the Church–Turing thesis ("thesis") involves the history of the development of the study of the nature of functions whose values are effectively calculable; or, in more modern terms, functions whose values are algorithmically computable. It is an important topic in modern mathematical theory and computer science, particularly associated with the work of Alonzo Church and Alan Turing.
The debate and discovery of the meaning of "computation" and "recursion" has been long and contentious | History of the Church–Turing thesis |
6,328 | Hypercomputation or super-Turing computation is a set of models of computation that can provide outputs that are not Turing-computable. For example, a machine that could solve the halting problem would be a hypercomputer; so too would one that can correctly evaluate every statement in Peano arithmetic.
The Church–Turing thesis states that any "computable" function that can be computed by a mathematician with a pen and paper using a finite set of simple algorithms, can be computed by a Turing machine | Hypercomputation |
6,329 | In computer science, interactive computation is a mathematical model for computation that involves input/output communication with the external world during computation.
Uses
Among the currently studied mathematical models of computation that attempt to capture interaction are Giorgi Japaridze's hard- and easy-play machines elaborated within the framework of computability logic, Dina Q. Goldin's Persistent Turing Machines (PTMs), and Yuri Gurevich's abstract state machines | Interactive computation |
6,330 | In mathematical logic, the intersection type discipline is a branch of type theory encompassing type systems that use the intersection type constructor
(
∩
)
{\displaystyle (\cap )}
to assign multiple types to a single term.
In particular, if a term
M
{\displaystyle M}
can be assigned both the type
φ
1
{\displaystyle \varphi _{1}}
and the type
φ
2
{\displaystyle \varphi _{2}}
, then
M
{\displaystyle M}
can be assigned the intersection type
φ
1
∩
φ
2
{\displaystyle \varphi _{1}\cap \varphi _{2}}
(and vice versa).
Therefore, the intersection type constructor can be used to express finite heterogeneous ad hoc polymorphism (as opposed to parametric polymorphism) | Intersection type discipline |
6,331 | The limits of computation are governed by a number of different factors. In particular, there are several physical and practical limits to the amount of computation or data storage that can be performed with a given amount of mass, volume, or energy.
Hardware limits or physical limits
Processing and memory density
The Bekenstein bound limits the amount of information that can be stored within a spherical volume to the entropy of a black hole with the same surface area | Limits of computation |
6,332 | In theoretical computer science, a Markov algorithm is a string rewriting system that uses grammar-like rules to operate on strings of symbols. Markov algorithms have been shown to be Turing-complete, which means that they are suitable as a general model of computation and can represent any mathematical expression from its simple notation. Markov algorithms are named after the Soviet mathematician Andrey Markov, Jr | Markov algorithm |
6,333 | In computability theory, the mortality problem is a decision problem related to the halting problem. For Turing machines, the halting problem can be stated as follows:
Given a Turing machine, and a word, decide whether the machine halts when run on the given word.
In contrast, the mortality problem for Turing machines asks whether all executions of the machine, starting from any configuration, halt | Mortality (computability theory) |
6,334 | In mathematical logic and computer science, a general recursive function, partial recursive function, or μ-recursive function is a partial function from natural numbers to natural numbers that is "computable" in an intuitive sense – as well as in a formal one. If the function is total, it is also called a total recursive function (sometimes shortened to recursive function). In computability theory, it is shown that the μ-recursive functions are precisely the functions that can be computed by Turing machines (this is one of the theorems that supports the Church–Turing thesis) | General recursive function |
6,335 | In mathematics and computer science, mutual recursion is a form of recursion where two mathematical or computational objects, such as functions or datatypes, are defined in terms of each other. Mutual recursion is very common in functional programming and in some problem domains, such as recursive descent parsers, where the datatypes are naturally mutually recursive.
Examples
Datatypes
The most important basic example of a datatype that can be defined by mutual recursion is a tree, which can be defined mutually recursively in terms of a forest (a list of trees) | Mutual recursion |
6,336 | A nomogram (from Greek nomos νόμος, "law" and grammē γραμμή, "line"), also called a nomograph, alignment chart, or abac, is a graphical calculating device, a two-dimensional diagram designed to allow the approximate graphical computation of a mathematical function. The field of nomography was invented in 1884 by the French engineer Philbert Maurice d'Ocagne (1862–1938) and used extensively for many years to provide engineers with fast graphical calculations of complicated formulas to a practical precision. Nomograms use a parallel coordinate system invented by d'Ocagne rather than standard Cartesian coordinates | Nomogram |
6,337 | In computer programming, a nondeterministic algorithm is an algorithm that, even for the same input, can exhibit different behaviors on different runs, as opposed to a deterministic algorithm. There are several ways an algorithm may behave differently from run to run. A concurrent algorithm can perform differently on different runs due to a race condition | Nondeterministic algorithm |
6,338 | In computability theory a numbering is the assignment of natural numbers to a set of objects such as functions, rational numbers, graphs, or words in some formal language. A numbering can be used to transfer the idea of computability and related concepts, which are originally defined on the natural numbers using computable functions, to these different types of objects.
Common examples of numberings include Gödel numberings in first-order logic, the description numbers that arise from universal Turing machines and admissible numberings of the set of partial computable functions | Numbering (computability theory) |
6,339 | In formal language theory within theoretical computer science, an infinite word is an infinite-length sequence (specifically, an ω-length sequence) of symbols, and an ω-language is a set of infinite words. Here, ω refers to the first ordinal number, the set of natural numbers.
Formal definition
Let Σ be a set of symbols (not necessarily finite) | Omega language |
6,340 | In computational complexity theory, the parallel computation thesis is a hypothesis which states that the time used by a (reasonable) parallel machine is polynomially related to the space used by a sequential machine. The parallel computation thesis was set forth by Chandra and Stockmeyer in 1976. In other words, for a computational model which allows computations to branch and run in parallel without bound, a formal language which is decidable under the model using no more than
t
(
n
)
{\displaystyle t(n)}
steps for inputs of length n is decidable by a non-branching machine using no more than
t
(
n
)
k
{\displaystyle t(n)^{k}}
units of storage for some constant k | Parallel computation thesis |
6,341 | The Post correspondence problem is an undecidable decision problem that was introduced by Emil Post in 1946. Because it is simpler than the halting problem and the Entscheidungsproblem it is often used in proofs of undecidability.
Definition of the problem
Let
A
{\displaystyle A}
be an alphabet with at least two symbols | Post correspondence problem |
6,342 | 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 can be determined 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 | Primitive recursive function |
6,343 | In mathematics, primitive recursive set functions or primitive recursive ordinal functions are analogs of primitive recursive functions, defined for sets or ordinals rather than natural numbers. They were introduced by Jensen & Karp (1971).
Definition
A primitive recursive set function is a function from sets to sets that can be obtained from the following basic functions by repeatedly applying the following rules of substitution and recursion:
The basic functions are:
Projection: Pn,m (x1, | Primitive recursive set function |
6,344 | Byzantine fault tolerant protocols are algorithms that are robust to arbitrary types of failures in distributed algorithms. The Byzantine agreement protocol is an essential part of this task. The constant-time quantum version of the Byzantine protocol, is described below | Quantum Byzantine agreement |
6,345 | Reachability analysis is a solution to the reachability problem in the particular context of distributed systems. It is used to determine which global states can be reached by a distributed system which consists of a certain number of local entities that communicated by the exchange of messages.
Overview
Reachability analysis was introduced in a paper of 1978 for the analysis and verification of communication protocols | Reachability analysis |
6,346 | Reachability is a fundamental problem that appears in several different contexts: finite- and infinite-state concurrent systems, computational models like cellular automata and Petri nets, program analysis, discrete and continuous systems, time critical systems, hybrid systems, rewriting systems, probabilistic and parametric systems, and open systems modelled as games. In general the reachability problem can be formulated as follows: Given a computational (potentially infinite state) system with a set of allowed rules or transformations, decide whether a certain state of a system is reachable from a given initial state of the system.
Variants of the reachability problem may result from additional constraints on the initial or final states, specific requirement for reachability paths as well as for iterative reachability or changing the questions into analysis of winning strategies in infinite games or unavoidability of some dynamics | Reachability problem |
6,347 | In computability theory, the theory of real computation deals with hypothetical computing machines using infinite-precision real numbers. They are given this name because they operate on the set of real numbers. Within this theory, it is possible to prove interesting statements such as "The complement of the Mandelbrot set is only partially decidable | Real computation |
6,348 | Recursion occurs when the definition of a concept or process depends on a simpler version of itself. Recursion is used in a variety of disciplines ranging from linguistics to logic. The most common application of recursion is in mathematics and computer science, where a function being defined is applied within its own definition | Recursion |
6,349 | In mathematics, logic and computer science, a formal language (a set of finite sequences of symbols taken from a fixed alphabet) is called recursive if it is a recursive subset of the set of all possible finite sequences over the alphabet of the language. Equivalently, a formal language is recursive if there exists a Turing machine that, when given a finite sequence of symbols as input, always halts and accepts it if it belongs to the language and halts and rejects it otherwise. In Theoretical computer science, such always-halting Turing machines are called total Turing machines or algorithms (Sipser 1997) | Recursive language |
6,350 | In mathematics, logic and computer science, a formal language is called recursively enumerable (also recognizable, partially decidable, semidecidable, Turing-acceptable or Turing-recognizable) if it is a recursively enumerable subset in the set of all possible words over the alphabet of the language, i. e. , if there exists a Turing machine which will enumerate all valid strings of the language | Recursively enumerable language |
6,351 | Rounding means replacing a number with an approximate value that has a shorter, simpler, or more explicit representation. For example, replacing $23. 4476 with $23 | Rounding |
6,352 | In computer science, a scale factor is a number used as a multiplier to represent a number on a different scale, functioning similarly to an exponent in mathematics. A scale factor is used when a real-world set of numbers needs to be represented on a different scale in order to fit a specific number format. Although using a scale factor extends the range of representable values, it also decreases the precision, resulting in rounding error for certain calculations | Scale factor (computer science) |
6,353 | Self-reference is a concept that involves referring to oneself or one's own attributes, characteristics, or actions. It can occur in language, logic, mathematics, philosophy, and other fields.
In natural or formal languages, self-reference occurs when a sentence, idea or formula refers to itself | Self-reference |
6,354 | In theoretical computer science and mathematical logic a string rewriting system (SRS), historically called a semi-Thue system, is a rewriting system over strings from a (usually finite) alphabet. Given a binary relation
R
{\displaystyle R}
between fixed strings over the alphabet, called rewrite rules, denoted by
s
→
t
{\displaystyle s\rightarrow t}
, an SRS extends the rewriting relation to all strings in which the left- and right-hand side of the rules appear as substrings, that is
u
s
v
→
u
t
v
{\displaystyle usv\rightarrow utv}
, where
s
{\displaystyle s}
,
t
{\displaystyle t}
,
u
{\displaystyle u}
, and
v
{\displaystyle v}
are strings.
The notion of a semi-Thue system essentially coincides with the presentation of a monoid | Semi-Thue system |
6,355 | Semiotic Engineering was originally proposed by Clarisse de Souza as a semiotic approach to designing user interface languages. Over the years, with research done at the Department of Informatics of the Pontifical Catholic University of Rio de Janeiro, it evolved into a semiotic theory of human-computer interaction (HCI). Semiotic Engineering views HCI as computer-mediated communication between designers and users at interaction time | Semiotic engineering |
6,356 | The shadow square, also known as an altitude scale, was an instrument used to determine the linear height of an object, in conjunction with the alidade, for angular observations. An early example was described in an Arabic treatise likely dating to 9th or 10th-century Baghdad. Shadow squares are often found on the backs of astrolabes | Shadow square |
6,357 | The simply typed lambda calculus (
λ
→
{\displaystyle \lambda ^{\to }}
), a form
of type theory, is a typed interpretation of the lambda calculus with only one type constructor (
→
{\displaystyle \to }
) that builds function types. It is the canonical and simplest example of a typed lambda calculus. The simply typed lambda calculus was originally introduced by Alonzo Church in 1940 as an attempt to avoid paradoxical use of the untyped lambda calculus | Simply typed lambda calculus |
6,358 | The size-change termination principle (SCT) guarantees termination for a computer program by proving that infinite computations always trigger infinite descent in data values that are well-founded. Size-change termination analysis utilizes this principle in order to solve the universal halting problem for a certain class of programs. When applied to general programs, the principle is intended to be used conservatively, which means that if the analysis determines that a program is terminating, the answer is sound, but a negative answer means "don't know" | Size-change termination principle |
6,359 | Ludwig Staiger is a German mathematician and computer scientist at the Martin Luther University of Halle-Wittenberg.
He received his Ph. D | Ludwig Staiger |
6,360 | The Stream X-machine (SXM) is a model of computation introduced by Gilbert Laycock in his 1993 PhD thesis, The Theory and Practice of Specification Based Software Testing.
Based on Samuel Eilenberg's X-machine, an extended finite-state machine for processing data of the type X, the Stream X-Machine is a kind of X-machine for processing a memory data type Mem with associated input and output streams In* and Out*, that is, where X = Out* × Mem × In*. The transitions of a Stream X-Machine are labelled by functions of the form φ: Mem × In → Out × Mem, that is, which compute an output value and update the memory, from the current memory and an input value | Stream X-Machine |
6,361 | In computability theory, super-recursive algorithms are a generalization of ordinary algorithms that are more powerful, that is, compute more than Turing machines. The term was introduced by Mark Burgin, whose book "Super-recursive algorithms" develops their theory and presents several mathematical models. Turing machines and other mathematical models of conventional algorithms allow researchers to find properties of recursive algorithms and their computations | Super-recursive algorithm |
6,362 | The Stream X-machine (SXM) is a model of computation introduced by Gilbert Laycock in his 1993 PhD thesis, The Theory and Practice of Specification Based Software Testing.
Based on Samuel Eilenberg's X-machine, an extended finite-state machine for processing data of the type X, the Stream X-Machine is a kind of X-machine for processing a memory data type Mem with associated input and output streams In* and Out*, that is, where X = Out* × Mem × In*. The transitions of a Stream X-Machine are labelled by functions of the form φ: Mem × In → Out × Mem, that is, which compute an output value and update the memory, from the current memory and an input value | Stream X-Machine |
6,363 | In computer science, a tail call is a subroutine call performed as the final action of a procedure. If the target of a tail is the same subroutine, the subroutine is said to be tail recursive, which is a special case of direct recursion. Tail recursion (or tail-end recursion) is particularly useful, and is often easy to optimize in implementations | Tail call |
6,364 | In computability theory and mathematical logic the Tarski–Kuratowski algorithm is a non-deterministic algorithm that produces an upper bound for the complexity of a given formula in the arithmetical hierarchy and analytical hierarchy.
The algorithm is named after Alfred Tarski and Kazimierz Kuratowski.
Algorithm
The Tarski–Kuratowski algorithm for the arithmetical hierarchy consists of the following steps:
Convert the formula to prenex normal form | Tarski–Kuratowski algorithm |
6,365 | Ten15 is an algebraically specified abstract machine. It was developed by Foster, Currie et al. at the Royal Signals and Radar Establishment at Malvern, Worcestershire, during the 1980s | Ten15 |
6,366 | In computational complexity theory, a transcomputational problem is a problem that requires processing of more than 1093 bits of information. Any number greater than 1093 is called a transcomputational number. The number 1093, called Bremermann's limit, is, according to Hans-Joachim Bremermann, the total number of bits processed by a hypothetical computer the size of the Earth within a time period equal to the estimated age of the Earth | Transcomputational problem |
6,367 | 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 decide other data-manipulation rule sets. Turing completeness is used as a way to express the power of such a data-manipulation rule set | Turing completeness |
6,368 | In computer science and mathematical logic the Turing degree (named after Alan Turing) or degree of unsolvability of a set of natural numbers measures the level of algorithmic unsolvability of the set.
Overview
The concept of Turing degree is fundamental in computability theory, where sets of natural numbers are often regarded as decision problems. The Turing degree of a set is a measure of how difficult it is to solve the decision problem associated with the set, that is, to determine whether an arbitrary number is in the given set | Turing degree |
6,369 | A Turing machine is a hypothetical computing device, first conceived by Alan Turing in 1936. Turing machines manipulate symbols on a potentially infinite strip of tape according to a finite table of rules, and they provide the theoretical underpinnings for the notion of a computer algorithm.
While none of the following models have been shown to have more power than the single-tape, one-way infinite, multi-symbol Turing-machine model, their authors defined and used them to investigate questions and solve problems more easily than they could have if they had stayed with Turing's a-machine model | Turing machine equivalents |
6,370 | A Turing tarpit (or Turing tar-pit) is any programming language or computer interface that allows for flexibility in function but is difficult to learn and use because it offers little or no support for common tasks. The phrase was coined in 1982 by Alan Perlis in the Epigrams on Programming:
54. Beware of the Turing tar-pit in which everything is possible but nothing of interest is easy | Turing tarpit |
6,371 | Turing's proof is a proof by Alan Turing, first published in January 1937 with the title "On Computable Numbers, with an Application to the Entscheidungsproblem". It was the second proof (after Church's theorem) of the negation of Hilbert's Entscheidungsproblem; that is, the conjecture that some purely mathematical yes–no questions can never be answered by computation; more technically, that some decision problems are "undecidable" in the sense that there is no single algorithm that infallibly gives a correct "yes" or "no" answer to each instance of the problem. In Turing's own words:
"what I shall prove is quite different from the well-known results of Gödel | Turing's proof |
6,372 | In computing, the Two Generals' Problem is a thought experiment meant to illustrate the pitfalls and design challenges of attempting to coordinate an action by communicating over an unreliable link. In the experiment, two generals are only able to communicate with one another by sending a messenger through enemy territory. The experiment asks how they might reach an agreement on the time to launch an attack, while knowing that any messenger they send could be captured | Two Generals' Problem |
6,373 | A typed lambda calculus is a typed formalism that uses the lambda-symbol (
λ
{\displaystyle \lambda }
) to denote anonymous function abstraction. In this context, types are usually objects of a syntactic nature that are assigned to lambda terms; the exact nature of a type depends on the calculus considered (see kinds below). From a certain point of view, typed lambda calculi can be seen as refinements of the untyped lambda calculus, but from another point of view, they can also be considered the more fundamental theory and untyped lambda calculus a special case with only one type | Typed lambda calculus |
6,374 | In computing (particularly, in programming), undefined value is a condition where an expression does not have a correct value, although it is syntactically correct. An undefined value must not be confused with empty string, Boolean "false" or other "empty" (but defined) values. Depending on circumstances, evaluation to an undefined value may lead to exception or undefined behaviour, but in some programming languages undefined values can occur during a normal, predictable course of program execution | Undefined value |
6,375 | Universality probability is an abstruse probability measure in computational complexity theory that concerns universal Turing machines.
Background
A Turing machine is a basic model of computation. Some Turing machines might be specific to doing particular calculations | Universality probability |
6,376 | Wang tiles (or Wang dominoes), first proposed by mathematician, logician, and philosopher Hao Wang in 1961, are a class of formal systems. They are modelled visually by square tiles with a color on each side. A set of such tiles is selected, and copies of the tiles are arranged side by side with matching colors, without rotating or reflecting them | Wang tile |
6,377 | The X-machine (XM) is a theoretical model of computation introduced by Samuel Eilenberg in 1974.
The X in "X-machine" represents the fundamental data type on which the machine operates; for example, a machine that operates on databases (objects of type database) would be a database-machine. The X-machine model is structurally the same as the finite-state machine, except that the symbols used to label the machine's transitions denote relations of type X→X | X-machine |
6,378 | The (Stream) X-Machine Testing Methodology is a complete functional testing approach to software- and hardware testing that exploits the scalability of the Stream X-Machine model of computation.
Using this methodology, it is likely to identify a finite test-set that exhaustively determines whether the tested system's implementation matches its specification. This goal is achieved by a divide-and-conquer approach, in which the design is decomposed by refinement into a collection of Stream X-Machines, which are implemented as separate modules, then tested bottom-up | X-Machine Testing |
6,379 | In cryptography and the theory of computation, Yao's test is a test defined by Andrew Chi-Chih Yao in 1982, against pseudo-random sequences. A sequence of words passes Yao's test if an attacker with reasonable computational power cannot distinguish it from a sequence generated uniformly at random.
Formal statement
Boolean circuits
Let
P
P
be a polynomial, and
S
=
{
S
k
}
k
{\displaystyle S=\{S_{k}\}_{k}}
be a collection of sets
S
k
S_{k}
of
P
(
k
)
P(k)
-bit long sequences, and for each
k
k
, let
μ
k
\mu _{k}
be a probability distribution on
S
k
S_{k}
, and
P
C
P_{C}
be a polynomial | Yao's test |
6,380 | Ritsuko Akagi (赤木リツコ, Akagi Ritsuko) is the head of the first section of the technology department at Nerv headquarters, and one of the main developers of Evangelion units in Hideaki Anno's 1995 mecha anime series Neon Genesis Evangelion. In 2005 during college, Ritsuko met Misato Katsuragi, who became her friend, and befriended her boyfriend Kaji, whom Ritsuko considered annoying. In 2008, after completing her studies at Tokyo-2, Ritsuko joined Gehirn Research Center as the head of Project E | Ritsuko Akagi |
6,381 | Ritsuko Akagi (赤木リツコ, Akagi Ritsuko) is the head of the first section of the technology department at Nerv headquarters, and one of the main developers of Evangelion units in Hideaki Anno's 1995 mecha anime series Neon Genesis Evangelion. In 2005 during college, Ritsuko met Misato Katsuragi, who became her friend, and befriended her boyfriend Kaji, whom Ritsuko considered annoying. In 2008, after completing her studies at Tokyo-2, Ritsuko joined Gehirn Research Center as the head of Project E | Ritsuko Akagi |
6,382 | Anthony "Tony" Almeida is a fictional character portrayed by Carlos Bernard on the television series 24. Almeida appeared in a total of 126 episodes (including 24: Legacy), the second highest number of episodes of any character in the series, third being Chloe O'Brian (125) and first being Jack Bauer (192), portrayed by Mary Lynn Rajskub and Kiefer Sutherland, respectively. Despite initially having friction with Jack Bauer, he eventually develops a strong friendship with Jack and becomes one of the few people Jack trusts unconditionally with his life | Tony Almeida |
6,383 | The following is a list of characters from the Spike Chunsoft video game series Danganronpa. The series follows the students of Hope's Peak Academy who are forced into a life of mutual killing by a sadistic teddy bear named Monokuma. The series consists of three games, Danganronpa: Trigger Happy Havoc, Danganronpa 2: Goodbye Despair and Danganronpa Another Episode: Ultra Despair Girls, along with a standalone sequel game, Danganronpa V3: Killing Harmony, various spin-off novels and manga including Danganronpa Zero and Killer Killer, and two anime television series, one an adaptation of the first game and the other a sequel and finale, Danganronpa 3: The End of Hope's Peak High School | List of Danganronpa characters |
6,384 | Cyborg (Victor Stone) is a superhero appearing in American comic books published by DC Comics. The character was created by writer Marv Wolfman and artist George Pérez, and first appeared in an insert preview in DC Comics Presents #26 (October 1980). Originally known as a member of the Teen Titans, Cyborg was established as a founding member of the Justice League in DC's 2011 reboot of its comic book titles | Cyborg (DC Comics) |
6,385 | Doctor Miles Bennett Dyson is a character in the sci-fi franchise Terminator. He is the original inventor of the microprocessor which would lead to the development of Skynet, an intelligent computer system intended to control the United States military, but which would later achieve sentience and launch a global war of extermination against humanity.
Dyson is portrayed by Joe Morton in Terminator 2: Judgment Day (T2), by Phil Morris in Terminator: The Sarah Connor Chronicles, and by Courtney B | Miles Dyson |
6,386 | Leopold James "Leo" Fitz is a fictional character that originated in the Marvel Cinematic Universe before appearing in Marvel Comics. The character, created by Joss Whedon, Jed Whedon and Maurissa Tancharoen, first appeared in the pilot episode of Agents of S. H | Leo Fitz |
6,387 | Seto Kaiba (Japanese: 海馬 瀬人, Hepburn: Kaiba Seto) is a fictional character in the manga Yu-Gi-Oh! by Kazuki Takahashi. As the majority shareholder and CEO of his own multi-national gaming company, Kaiba Corporation, Kaiba is reputed to be Japan's greatest gamer and aims to become the world's greatest player of the American card game, Duel Monsters (Magic & Wizards in the Japanese manga). In all mediums, his arch-rival is the protagonist of the series, Yugi Mutou, who is also a superb game player | Seto Kaiba |
6,388 | Dr. Liara T'Soni is a fictional character in BioWare's Mass Effect franchise, who serves as a party member (or "squadmate") in the original Mass Effect trilogy. She is an asari, a female-appearing species from the planet Thessia who are naturally inclined towards biotics, the ability to "manipulate dark energy and create mass effect fields through the use of electrical impulses from the brain" | Liara T'Soni |
6,389 | Apu Nahasapeemapetilon is a recurring character in the American animated television series The Simpsons. He is an Indian immigrant proprietor who runs the Kwik-E-Mart, a popular convenience store in Springfield, and is known for his catchphrase, "Thank you, come again". He was voiced by Hank Azaria and first appeared in the episode "The Telltale Head" | Apu Nahasapeemapetilon |
6,390 | Walter O'Brien is the fictional lead character in the American drama television series, Scorpion. The character is inspired by the Irish businessman and information technologist of the same name. The character, played by actor Elyes Gabel, follows a loose trajectory of Walter O'Brien's real-life exploits that thwart terrorism and disasters in each episode of the series | Walter O'Brien (Scorpion) |
6,391 | Phyllis Summers is a fictional character from The Young and the Restless, an American soap opera on the CBS network. The character was created and introduced by William J. Bell, and debuted in the episode airing on October 18, 1994 | Phyllis Summers |
6,392 | This is a list of computer scientists, people who do work in computer science, in particular researchers and authors.
Some persons notable as programmers are included here because they work in research as well as program. A few of these people pre-date the invention of the digital computer; they are now regarded as computer scientists because their work can be seen as leading to the invention of the computer | List of computer scientists |
6,393 | African-American women in computer science were among early pioneers in computing in the United States, and there are notable African-American women working in computer science.
History
African-American women were hired as mathematicians to do technical computing needed to support aeronautical and other research. They included such women as Katherine G | African-American women in computer science |
6,394 | This is a list of people in blockchain technology, people who do work in the area of Blockchain and Cryptocurrency, in particular researchers, business people, and authors.
Some people that are notable as programmers are included here because they work in research as well as programming. A few of these people pre-date the invention of this technology; they are now regarded as people in blockchain technology because their work can be seen as leading to the invention of this technology | List of people in blockchain technology |
6,395 | Instead of having a single "inventor", the Internet was developed by many people over many years. The following are some Internet pioneers who contributed to its early and ongoing development. These include early theoretical foundations, specifying original protocols, and expansion beyond a research tool to wide deployment | List of Internet pioneers |
6,396 | This is a list of notable Jewish American computer scientists. For other Jewish Americans, see Lists of Jewish Americans.
Hal Abelson, artificial intelligence
Leonard Adleman, RSA cryptography, DNA computing, Turing Award (2002)
Adi Shamir, RSA cryptography, DNA computing, Turing Award (2002)
Paul Baran, Polish-born engineer; co-invented packet switching
Lenore and Manuel Blum (Turing Award (1995)), Venezuelan-American computer scientist; computational complexity, parents of Avrim Blum (Co-training)
Dan Bricklin, creator of the original spreadsheet
Sergey Brin, co-founder of Google
Danny Cohen, Israeli-American Internet pioneer; first to run a visual flight simulator across the ARPANet
Robert Fano, Italian-American information theorist
Ed Feigenbaum, artificial intelligence, Turing Award (1994)
William F | List of Jewish American computer scientists |
6,397 | Many notable computer scientists and others have been associated with the Palo Alto Research Center Incorporated (PARC), formerly Xerox PARC. They include:
Nina Amenta (at PARC 1996–1997), researcher in computational geometry and computer graphics
Anne Balsamo (at PARC 1999–2002), media studies scholar of connections between art, culture, gender, and technology
Patrick Baudisch (at PARC 2000–2001), in human–computer interaction
Daniel G. Bobrow (at PARC 1972–2017), artificial intelligence researcher
Susanne Bødker (at PARC 1982–1983), researcher in human–computer interaction
David Boggs (at PARC 1972–1982), computer network pioneer, coinventor of Ethernet
Anita Borg (at PARC 1997–2003), computer systems researcher, advocate for women in computing
John Seely Brown (at PARC 1978–2000), researcher in organizational studies, chief scientist of Xerox
Bill Buxton (at PARC 1989–1994), pioneer in human–computer interaction
Stuart Card (at PARC 1974-2010), applied human factors in human–computer interaction
Robert Carr (at PARC in late 1970s), CAD and office software designer
Ed Chi (at PARC 1997–2011), researcher in information visualization and the usability of web sites
Elizabeth F | List of people associated with PARC |
6,398 | This is a list of people who made transformative breakthroughs in the creation, development and imagining of what computers could do.
Pioneers
To arrange the list either chronologically by year or alphabetically by person (ascending or descending), click that column's small "up-down" icon. ~ Items marked with a tilde are circa dates | List of pioneers in computer science |
6,399 | This is a list of programmers notable for their contributions to software, either as original author or architect, or for later additions. All entries must already have associated articles.
A
Michael Abrash – program optimization and x86 assembly language
Scott Adams – series of text adventures beginning in the late 1970s
Tarn Adams – Dwarf Fortress
Leonard Adleman – co-created RSA algorithm (being the A in that name), coined the term computer virus
Alfred Aho – co-created AWK (being the A in that name), and main author of famous Compilers: Principles, Techniques, and Tools (Dragon book)
Andrei Alexandrescu – author, expert on languages C++, D
Paul Allen – Altair BASIC, Applesoft BASIC, cofounded Microsoft
Eric Allman – sendmail, syslog
Marc Andreessen – co-created Mosaic, cofounded Netscape
Jeremy Ashkenas – CoffeeScript programming language and Backbone | List of programmers |
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