Polynomial-time reductionIn computational complexity theory, a polynomial-time reduction is a method for solving one problem using another. One shows that if a hypothetical subroutine solving the second problem exists, then the first problem can be solved by transforming or reducing it to inputs for the second problem and calling the subroutine one or more times. If both the time required to transform the first problem to the second, and the number of times the subroutine is called is polynomial, then the first problem is polynomial-time reducible to the second.
Reduction (complexity)In computability theory and computational complexity theory, a reduction is an algorithm for transforming one problem into another problem. A sufficiently efficient reduction from one problem to another may be used to show that the second problem is at least as difficult as the first. Intuitively, problem A is reducible to problem B, if an algorithm for solving problem B efficiently (if it existed) could also be used as a subroutine to solve problem A efficiently. When this is true, solving A cannot be harder than solving B.
Many-one reductionIn computability theory and computational complexity theory, a many-one reduction (also called mapping reduction) is a reduction which converts instances of one decision problem (whether an instance is in ) to another decision problem (whether an instance is in ) using an effective function. The reduced instance is in the language if and only if the initial instance is in its language . Thus if we can decide whether instances are in the language , we can decide whether instances are in its language by applying the reduction and solving .
Turing reductionIn computability theory, a Turing reduction from a decision problem to a decision problem is an oracle machine which decides problem given an oracle for (Rogers 1967, Soare 1987). It can be understood as an algorithm that could be used to solve if it had available to it a subroutine for solving . The concept can be analogously applied to function problems. If a Turing reduction from to exists, then every algorithm for can be used to produce an algorithm for , by inserting the algorithm for at each place where the oracle machine computing queries the oracle for .
Log-space reductionIn computational complexity theory, a log-space reduction is a reduction computable by a deterministic Turing machine using logarithmic space. Conceptually, this means it can keep a constant number of pointers into the input, along with a logarithmic number of fixed-size integers. It is possible that such a machine may not have space to write down its own output, so the only requirement is that any given bit of the output be computable in log-space. Formally, this reduction is executed via a log-space transducer.
P-completeIn computational complexity theory, a decision problem is P-complete (complete for the complexity class P) if it is in P and every problem in P can be reduced to it by an appropriate reduction. The notion of P-complete decision problems is useful in the analysis of: which problems are difficult to parallelize effectively, which problems are difficult to solve in limited space. specifically when stronger notions of reducibility than polytime-reducibility are considered.
Complete informationIn economics and game theory, complete information is an economic situation or game in which knowledge about other market participants or players is available to all participants. The utility functions (including risk aversion), payoffs, strategies and "types" of players are thus common knowledge. Complete information is the concept that each player in the game is aware of the sequence, strategies, and payoffs throughout gameplay.
PSPACE-completeIn computational complexity theory, a decision problem is PSPACE-complete if it can be solved using an amount of memory that is polynomial in the input length (polynomial space) and if every other problem that can be solved in polynomial space can be transformed to it in polynomial time. The problems that are PSPACE-complete can be thought of as the hardest problems in PSPACE, the class of decision problems solvable in polynomial space, because a solution to any one such problem could easily be used to solve any other problem in PSPACE.
Information asymmetryIn contract theory and economics, information asymmetry deals with the study of decisions in transactions where one party has more or better information than the other. Information asymmetry creates an imbalance of power in transactions, which can sometimes cause the transactions to be inefficient, causing market failure in the worst case. Examples of this problem are adverse selection, moral hazard, and monopolies of knowledge. A common way to visualise information asymmetry is with a scale, with one side being the seller and the other the buyer.
Polynomial hierarchyIn computational complexity theory, the polynomial hierarchy (sometimes called the polynomial-time hierarchy) is a hierarchy of complexity classes that generalize the classes NP and co-NP. Each class in the hierarchy is contained within PSPACE. The hierarchy can be defined using oracle machines or alternating Turing machines. It is a resource-bounded counterpart to the arithmetical hierarchy and analytical hierarchy from mathematical logic. The union of the classes in the hierarchy is denoted PH.
Extensive-form gameIn game theory, an extensive-form game is a specification of a game allowing (as the name suggests) for the explicit representation of a number of key aspects, like the sequencing of players' possible moves, their choices at every decision point, the (possibly imperfect) information each player has about the other player's moves when they make a decision, and their payoffs for all possible game outcomes. Extensive-form games also allow for the representation of incomplete information in the form of chance events modeled as "moves by nature".
P (complexity)In computational complexity theory, P, also known as PTIME or DTIME(nO(1)), is a fundamental complexity class. It contains all decision problems that can be solved by a deterministic Turing machine using a polynomial amount of computation time, or polynomial time. Cobham's thesis holds that P is the class of computational problems that are "efficiently solvable" or "tractable". This is inexact: 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.
Perfect informationIn economics, perfect information (sometimes referred to as "no hidden information") is a feature of perfect competition. With perfect information in a market, all consumers and producers have complete and instantaneous knowledge of all market prices, their own utility, and own cost functions. In game theory, a sequential game has perfect information if each player, when making any decision, is perfectly informed of all the events that have previously occurred, including the "initialization event" of the game (e.
Polynomial-time approximation schemeIn computer science (particularly algorithmics), a polynomial-time approximation scheme (PTAS) is a type of approximation algorithm for optimization problems (most often, NP-hard optimization problems). A PTAS is an algorithm which takes an instance of an optimization problem and a parameter ε > 0 and produces a solution that is within a factor 1 + ε of being optimal (or 1 – ε for maximization problems). For example, for the Euclidean traveling salesman problem, a PTAS would produce a tour with length at most (1 + ε)L, with L being the length of the shortest tour.
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).
Exponential growthExponential growth is a process that increases quantity over time. It occurs when the instantaneous rate of change (that is, the derivative) of a quantity with respect to time is proportional to the quantity itself. Described as a function, a quantity undergoing exponential growth is an exponential function of time, that is, the variable representing time is the exponent (in contrast to other types of growth, such as quadratic growth).
GameA game is a structured form of play, usually undertaken for entertainment or fun, and sometimes used as an educational tool. Many games are also considered to be work (such as professional players of spectator sports or games) or art (such as jigsaw puzzles or games involving an artistic layout such as Mahjong, solitaire, or some video games). Games are sometimes played purely for enjoyment, sometimes for achievement or reward as well. They can be played alone, in teams, or online; by amateurs or by professionals.
Noise reductionNoise reduction is the process of removing noise from a signal. Noise reduction techniques exist for audio and images. Noise reduction algorithms may distort the signal to some degree. Noise rejection is the ability of a circuit to isolate an undesired signal component from the desired signal component, as with common-mode rejection ratio. All signal processing devices, both analog and digital, have traits that make them susceptible to noise.
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.
ConstructionConstruction is a general term meaning the art and science to form objects, systems, or organizations, and comes from Latin constructio (from com- "together" and struere "to pile up") and Old French construction. To construct is the verb: the act of building, and the noun is construction: how something is built, the nature of its structure. In its most widely used context, construction covers the processes involved in delivering buildings, infrastructure, industrial facilities, and associated activities through to the end of their life.
