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If there is an algorithm (say a Turing machine, or a computer program with unbounded memory) that produces the correct answer for any input string of length n in at most cn k steps, where k and c are constants independent of the input string, then we say that the problem can be solved in polynomial time and we place it in the class P. Formally ...
A decision problem is a computational problem where the answer for every instance is either yes or no. An example of a decision problem is primality testing: "Given a positive integer n, determine if n is prime." A decision problem is typically represented as the set of all instances for which the answer is yes. For example, primality testing ...
An automaton processes one input picked from a set of symbols or letters, which is called an input alphabet. The symbols received by the automaton as input at any step are a sequence of symbols called words. An automaton has a set of states. At each moment during a run of the automaton, the automaton is in one of its states.
An example of a decision problem is the following. The input is an arbitrary graph. The problem consists in deciding whether the given graph is connected or not. The formal language associated with this decision problem is then the set of all connected graphs — to obtain a precise definition of this language, one has to decide how graphs are ...
The universal halting problem, also known (in recursion theory) as totality, is the problem of determining whether a given computer program will halt for every input (the name totality comes from the equivalent question of whether the computed function is total). This problem is not only undecidable, as the halting problem is, but highly ...
In computer science, the general meaning of input is to provide or give something to the computer, in other words, when a computer or device is receiving a command or signal from outer sources, the event is referred to as input to the device. Some computer devices can also be categorized as input devices, [1] because devices are used to send ...
In computer science, a deterministic algorithm is an algorithm that, given a particular input, will always produce the same output, with the underlying machine always passing through the same sequence of states. Deterministic algorithms are by far the most studied and familiar kind of algorithm, as well as one of the most practical, since they ...
Computational mathematics is the study of the interaction between mathematics and calculations done by a computer. [1] A large part of computational mathematics consists roughly of using mathematics for allowing and improving computer computation in areas of science and engineering where mathematics are useful.