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 . ....
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.
2D computer graphics2D computer graphics is the generation of s—mostly from two-dimensional models (such as 2D geometric models, text, and digital images) and by techniques specific to them. It may refer to the branch of computer science that comprises such techniques or to the models themselves. 2D computer graphics are mainly used in applications that were originally developed upon traditional printing and drawing technologies, such as typography, cartography, technical drawing, advertising, etc.
Big O notationBig O notation is a mathematical notation that describes the limiting behavior of a function when the argument tends towards a particular value or infinity. Big O is a member of a family of notations invented by Paul Bachmann, Edmund Landau, and others, collectively called Bachmann–Landau notation or asymptotic notation. The letter O was chosen by Bachmann to stand for Ordnung, meaning the order of approximation. In computer science, big O notation is used to classify algorithms according to how their run time or space requirements grow as the input size grows.
NP-completenessIn computational complexity theory, a problem is NP-complete when: It is a decision problem, meaning that for any input to the problem, the output is either "yes" or "no". When the answer is "yes", this can be demonstrated through the existence of a short (polynomial length) solution. The correctness of each solution can be verified quickly (namely, in polynomial time) and a brute-force search algorithm can find a solution by trying all possible solutions.
NP-hardnessIn computational complexity theory, NP-hardness (non-deterministic polynomial-time hardness) is the defining property of a class of problems that are informally "at least as hard as the hardest problems in NP". A simple example of an NP-hard problem is the subset sum problem. A more precise specification is: a problem H is NP-hard when every problem L in NP can be reduced in polynomial time to H; that is, assuming a solution for H takes 1 unit time, Hs solution can be used to solve L in polynomial time.
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.
P versus NP problemThe P versus NP problem is a major unsolved problem in theoretical computer science. In informal terms, it asks whether every problem whose solution can be quickly verified can also be quickly solved. The informal term quickly, used above, means the existence of an algorithm solving the task that runs in polynomial time, such that the time to complete the task varies as a polynomial function on the size of the input to the algorithm (as opposed to, say, exponential time).
Time complexityIn computer science, the time complexity is the computational complexity that describes the amount of computer time it takes to run an algorithm. Time complexity is commonly estimated by counting the number of elementary operations performed by the algorithm, supposing that each elementary operation takes a fixed amount of time to perform. Thus, the amount of time taken and the number of elementary operations performed by the algorithm are taken to be related by a constant factor.
PenA pen is a common writing instrument that applies ink to a surface, usually paper, for writing or drawing. Early pens such as reed pens, quill pens, dip pens and ruling pens held a small amount of ink on a nib or in a small void or cavity which had to be periodically recharged by dipping the tip of the pen into an inkwell. Today, such pens find only a small number of specialized uses, such as in illustration and calligraphy. Reed pens, quill pens and dip pens, which were used for writing, have been replaced by ballpoint pens, rollerball pens, fountain pens and felt or ceramic tip pens.
QuillA quill is a writing tool made from a moulted flight feather (preferably a primary wing-feather) of a large bird. Quills were used for writing with ink before the invention of the dip pen, the metal-nibbed pen, the fountain pen, and, eventually, the ballpoint pen. As with the earlier reed pen (and later dip pen), a quill has no internal ink reservoir and therefore needs to periodically be dipped into an inkwell during writing. The hand-cut goose quill is rarely used as a calligraphy tool anymore because many papers are now derived from wood pulp and would quickly wear a quill down.
ComplexityComplexity characterises the behaviour of a system or model whose components interact in multiple ways and follow local rules, leading to non-linearity, randomness, collective dynamics, hierarchy, and emergence. The term is generally used to characterize something with many parts where those parts interact with each other in multiple ways, culminating in a higher order of emergence greater than the sum of its parts. The study of these complex linkages at various scales is the main goal of complex systems theory.
