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.

In computational complexity theory, BQP ( bounded error quantum polynomial time ) is the class of decision problems solvable by a quantum computer 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.

In the field of artificial intelligence, the most difficult problems are informally known as AI-complete or AI-hard, implying that the difficulty of these computational problems is equivalent to solving the central artificial intelligence problem — making computers as intelligent as people, or strong AI.

* Collision detection, the computational problem of detecting the intersection of two or more objects

In this context, a computational problem is understood to be a task that is in principle amenable to being solved by a computer ( i. e. the problem can be stated by a set of mathematical instructions ).

Informally, a computational problem consists of problem instances and solutions to these problem instances.

A computational problem can be viewed as an infinite collection of instances together with a solution for every instance.

The input string for a computational problem is referred to as a problem instance, and should not be confused with the problem itself.

When considering computational problems, a problem instance is a string over an alphabet.

" Difficult ", in this sense, is described in terms of the computational resources needed by the most efficient algorithm for a certain problem.

A distributed system may have a common goal, such as solving a large computational problem.

In mathematics and computational geometry, a Delaunay triangulation for a set P of points in a plane is a triangulation DT ( P ) such that no point in P is inside the circumcircle of any triangle in DT ( P ).

In 1982, the so-called TTAPS team ( Richard P. Turco, Owen Toon, Thomas P. Ackerman, James B. Pollack and Carl Sagan ) undertook a computational modeling study of the atmospheric consequences of nuclear war, publishing their results in Science in December 1983.

In computational complexity theory, the complexity class # P ( pronounced " number P " or, sometimes " sharp P " or " hash P ") is the set of the counting problems associated with the decision problems in the set NP.

# P-complete, pronounced " sharp P complete " or " number P complete " is a complexity class in computational complexity theory.

In complexity theory, computational problems that are co-NP-complete are those that are the hardest problems in co-NP, in the sense that they are the ones most likely not to be in P. If there exists a way to solve a co-NP-complete problem quickly, then that algorithm can be used to solve all co-NP problems quickly.

However, the time hierarchy theorems provide no means to relate deterministic and non-deterministic complexity, or time and space complexity, so they cast no light on the great unsolved questions of computational complexity theory: whether P and NP, NP and PSPACE, PSPACE and EXPTIME, or EXPTIME and NEXPTIME are equal or not.

* 1975 – R. P. Poplavskii publishes " Thermodynamical models of information processing " ( in Russian ), Uspekhi Fizicheskikh Nauk, 115: 3, 465 – 501 which showed the computational infeasibility of simulating quantum systems on classical computers, due to the superposition principle.

The chemical analysis revealed that traces of Mn, S, Si, and Pb were present and provided computational formulas of ( Ba < sub > 4. 68 </ sub > Sr < sub > 0. 19 </ sub > Ca < sub > 0. 13 </ sub >)( P < sub > 2. 98 </ sub > Si < sub > 0. 01 </ sub >) O < sub > 11. 96 </ sub >( C < sub > l0. 99 </ sub > F < sub > 0. 05 </ sub >) and ( Ba < sub > 4. 05 </ sub > Ca < sub > 0. 75 </ sub > Sr < sub > 0. 24 </ sub > Pb < sub > 0. 03 </ sub >)( P < sub > 2. 94 </ sub > Si < sub > 0. 01 </ sub >) O < sub > 11. 93 </ sub >( Cl < sub > 0. 93 </ sub > F < sub > 0. 14 </ sub >).

Nondeterministic machines have become a key concept in computational complexity theory, particularly with the description of complexity classes P and NP.

Other work centers on fragments of arithmetic, studying the divide between those theories interpretable in Raphael Robinson's Arithmetic and those that are not ; computational complexity, including the problem of whether P is equal to NP or not ; and automated proof checking.

Other connections to unparameterised computational complexity are that FPT equals W if and only if circuit satisfiability can be decided in time, or if and only if there is a computable, nondecreasing, unbounded function f such that all languages recognised by a nondeterministic polynomial-time Turing machine using f ( n ) log n nondeterministic choices are in P.

In computational complexity theory, P, also known as PTIME or DTIME ( n < sup > O ( 1 )</ sup >), is one of the most fundamental complexity classes.

Cobham's thesis holds that P is the class of computational problems which are " efficiently solvable " or " tractable "; in practice, some problems not known to be in P have practical solutions, and some that are in P do not, but this is a useful rule of thumb.