In algorithmic information theory ( a subfield of computer science ), the Kolmogorov complexity of an object, such as a piece of text, is a measure of the computational resources needed to specify the object.

Algorithm analysis is an important part of a broader computational complexity theory, which provides theoretical estimates for the resources needed by any algorithm which solves a given computational problem.

Computational complexity theory deals with the relative computational difficulty of computable functions.

In computational complexity theory, BPP, which stands for bounded-error probabilistic polynomial time is the class of decision problems solvable by a probabilistic Turing machine in polynomial time, with an error probability of at most 1 / 3 for all instances.

Some, such as computational complexity theory, which studies fundamental properties of computational problems, are highly abstract, while others, such as computer graphics, emphasize real-world applications.

Some fields, such as computational complexity theory ( which explores the fundamental properties of computational problems ), are highly abstract, whilst fields such as computer graphics emphasise real-world applications.

In computational complexity theory, co-NP is a complexity class.

* Complexity class, a set of problems of related complexity in computational complexity theory

Computational complexity theory is a branch of the theory of computation in theoretical computer science and mathematics that focuses on classifying computational problems according to their inherent difficulty, and relating those classes to each other.

One of the roles of computational complexity theory is to determine the practical limits on what computers can and cannot do.

A key distinction between analysis of algorithms and computational complexity theory is that the former is devoted to analyzing the amount of resources needed by a particular algorithm to solve a problem, whereas the latter asks a more general question about all possible algorithms that could be used to solve the same problem.

In turn, imposing restrictions on the available resources is what distinguishes computational complexity from computability theory: the latter theory asks what kind of problems can, in principle, be solved algorithmically.

In computational complexity theory, a problem refers to the abstract question to be solved.

For this reason, complexity theory addresses computational problems and not particular problem instances.

He contributed to the development of the rigorous analysis of the computational complexity of algorithms and systematized formal mathematical techniques for it.

* Knuth's article about the computational complexity of songs, " The Complexity of Songs ", was reprinted twice in computer science journals.

In computability theory and computational complexity theory, a decision problem is a question in some formal system with a yes-or-no answer, depending on the values of some input parameters.

The field of computational complexity categorizes decidable decision problems by how difficult they are to solve.

Hayek's argumentation is not only regarding computational complexity for the central planners, however.

His mathematical specialties were noncommutative ring theory and computational algebra and its applications, including automated theorem proving in geometry.

Bioinformatics now entails the creation and advancement of databases, algorithms, computational and statistical techniques and theory to solve formal and practical problems arising from the management and analysis of biological data.

Since the desired effect is computational difficulty, in theory one would choose an algorithm and desired difficulty level, thus decide the key length accordingly.

A computer scientist specialises in the theory of computation and the design of computers or computational systems.

# the computational theory, specifying the goals of the computation ;

The subsequent development of category theory was powered first by the computational needs of homological algebra, and later by the axiomatic needs of algebraic geometry, the field most resistant to being grounded in either axiomatic set theory or the Russell-Whitehead view of united foundations.

The origins of cognitive thinking such as computational theory of mind can be traced back as early as Descartes in the 17th century, and proceeding up to Alan Turing in the 1940s and ' 50s.

It is a challenge to functionalism and the computational theory of mind, and is related to such questions as the mind-body problem, the problem of other minds, the symbol-grounding problem, and the hard problem of consciousness.

The concept of bounded rationality revises this assumption to account for the fact that perfectly rational decisions are often not feasible in practice because of the finite computational resources available for making them.

The prover is all-powerful and possesses unlimited computational resources, but cannot be trusted, while the verifier has bounded computation power.

In computational complexity theory, a probabilistically checkable proof ( PCP ) is a type of proof that can be checked by a randomized algorithm using a bounded amount of randomness and reading a bounded number of bits of the proof.

Dembski appeals to cryptographic practice in support of the concept of the universal probability bound, noting that cryptographers have sometimes compared the security of encryption algorithms against brute force attacks by the likelihood of success of an adversary utilizing computational resources bounded by very large physical constraints.

The goal of computational chemistry is to minimize this residual error while keeping the calculations tractable.

Even if this process is more complex than analog processing and has a discrete value range, the application of computational power to digital signal processing allows for many advantages over analog processing in many applications, such as error detection and correction in transmission as well as data compression.

The chaotic nature of the atmosphere, the massive computational power required to solve the equations that describe the atmosphere, error involved in measuring the initial conditions, and an incomplete understanding of atmospheric processes mean that forecasts become less accurate as the difference in current time and the time for which the forecast is being made ( the range of the forecast ) increases.

Important potential properties of statistics include completeness, consistency, sufficiency, unbiasedness, minimum mean square error, low variance, robustness, and computational convenience.

The chaotic nature of the atmosphere, the massive computational power required to solve the equations that describe the atmosphere, error involved in measuring the initial conditions, and an incomplete understanding of atmospheric processes mean that forecasts become less accurate as the difference in current time and the time for which the forecast is being made ( the range of the forecast ) increases.

( In computational mechanics, when solving a system such as Ax = b there is a distinction between the " error " — the inaccuracy in x — and residual — the inaccuracy in Ax.

The chaotic nature of the atmosphere, the massive computational power required to solve the equations that describe the atmosphere, error involved in measuring the initial conditions, and an incomplete understanding of atmospheric processes mean that forecasts become less accurate as the difference in current time and the time for which the forecast is being made ( the range of the forecast ) increases.

Practitioners who come into CALL via the disciplines of computational linguistics, e. g. Natural Language Processing ( NLP ) and Human Language Technologies ( HLT ), tend to be more optimistic about the potential of error analysis by computer than those who come into CALL via language teaching.

Typically, algorithms would approach the right solution in the limit, if there were no round-off or truncation errors, but depending on the specific computational method, errors can be magnified, instead of damped, causing the error to grow exponentially.

In engineering and computational mechanics, the word bias is sometimes used as a synonym of systematic error.

Postwar analysis of the Silbervogel design involving a mathematical control analysis unearthed a computational error and it turned out that the heat flow during the initial re-entry would have been far higher than originally calculated by Sänger and Bredt ; if the Silbervogel had been constructed according to their flawed calculations the craft would have been destroyed during re-entry.

In numerical analysis, computational physics, and simulation, discretization error ( or truncation error ) is error resulting from the fact that a function of a continuous variable is represented in the computer by a finite number of evaluations, for example, on a lattice.

Discretization error can usually be reduced by using a more finely spaced lattice, with an increased computational cost.

Discretization error is the principal source of error in methods of finite differences and the pseudo-spectral method of computational physics.

* It can be computational ( i. e. based on some mathematical problem, like factoring ) or unconditional ( usually with some probability of error which can be made arbitrarily small ).

Girard shows that for second-order affine linear logic, given a computational system with nontermination and error stops as effects, realizability and focalization give the same meaning to types.

In computational complexity theory, RL ( Randomized Logarithmic-space ), sometimes called RLP ( Randomized Logarithmic-space Polynomial-time ), is the complexity class of problems solvable in logarithmic space and polynomial time with probabilistic Turing machines with one-sided error.

In computational chemistry, a dangling bond is an error in structure creation, in which an atom is inadvertently drawn with too few bonding partners, or a bond is mistakenly drawn with an atom at only one end.

# numerical mathematical methods that traditionally prove unsuccessful due to buildup of computational error ;