In mathematics and computer science, an algorithm is a finite sequence of rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for performing calculations and data processing. By making use of artificial intelligence, algorithms can perform automated deductions and use mathematical and logical tests to divert the code execution through various routes. Using human characteristics as descriptors of machines in metaphorical ways was already practiced by Alan Turing with terms such as "memory", "search" and "stimulus".
In complexity theory and computability theory, an oracle machine is an abstract machine used to study decision problems. It can be visualized as a Turing machine with a black box, called an oracle, which is able to solve certain problems in a single operation. The problem can be of any complexity class. Even undecidable problems, such as the halting problem, can be used.
A Turing machine is a mathematical model of computation describing an abstract machine that manipulates symbols on a strip of tape according to a table of rules. Despite the model's simplicity, it is capable of implementing any computer algorithm.
In computer science, a universal Turing machine (UTM) is a Turing machine that simulates an arbitrary Turing machine on arbitrary input. The universal machine essentially achieves this by reading both the description of the machine to be simulated as well as the input to that machine from its own tape. Alan Turing introduced the idea of such a machine in 1936–1937. This principle is considered to be the origin of the idea of a stored-program computer used by John von Neumann in 1946 for the "Electronic Computing Instrument" that now bears von Neumann's name: the von Neumann architecture.
A one-instruction set computer (OISC), sometimes called an ultimate reduced instruction set computer (URISC), is an abstract machine that uses only one instruction – obviating the need for a machine language opcode. With a judicious choice for the single instruction and given infinite resources, an OISC is capable of being a universal computer in the same manner as traditional computers that have multiple instructions. OISCs have been recommended as aids in teaching computer architecture and have been used as computational models in structural computing research. The first carbon nanotube computer is a 1-bit one-instruction set computer.
A tag system is a deterministic computational model published by Emil Leon Post in 1943 as a simple form of a Post canonical system. A tag system may also be viewed as an abstract machine, called a Post tag machine —briefly, a finite-state machine whose only tape is a FIFO queue of unbounded length, such that in each transition the machine reads the symbol at the head of the queue, deletes a constant number of symbols from the head, and appends to the tail a symbol-string that depends solely on the first symbol read in this transition.
Computability is the ability to solve a problem in an effective manner. It is a key topic of the field of computability theory within mathematical logic and the theory of computation within computer science. The computability of a problem is closely linked to the existence of an algorithm to solve the problem.
In mathematical logic and theoretical computer science a register machine is a generic class of abstract machines used in a manner similar to a Turing machine. All the models are Turing equivalent.
In computer science, random-access machine (RAM) is an abstract machine in the general class of register machines. The RAM is very similar to the counter machine but with the added capability of 'indirect addressing' of its registers. Like the counter machine, The RAM has its instructions in the finite-state portion of the machine.
A Post–Turing machine is a "program formulation" of a type of Turing machine, comprising a variant of Emil Post's Turing-equivalent model of computation. Post's model and Turing's model, though very similar to one another, were developed independently. Turing's paper was received for publication in May 1936, followed by Post's in October.) A Post–Turing machine uses a binary alphabet, an infinite sequence of binary storage locations, and a primitive programming language with instructions for bi-directional movement among the storage locations and alteration of their contents one at a time. The names "Post–Turing program" and "Post–Turing machine" were used by Martin Davis in 1973–1974. Later in 1980, Davis used the name "Turing–Post program".
Turing's proof is a proof by Alan Turing, first published in January 1937 with the title "On Computable Numbers, with an Application to the Entscheidungsproblem. It was the second proof of the negation of Hilbert's Entscheidungsproblem; that is, the conjecture that some purely mathematical yes–no questions can never be answered by computation; more technically, that some decision problems are "undecidable" in the sense that there is no single algorithm that infallibly gives a correct "yes" or "no" answer to each instance of the problem. In Turing's own words: "what I shall prove is quite different from the well-known results of Gödel ... I shall now show that there is no general method which tells whether a given formula U is provable in K [Principia Mathematica]".
In theoretical computer science a pointer machine is an "atomistic" abstract computational machine model akin to the random-access machine. A pointer algorithm is an algorithm restricted to the pointer machine model.
The following are examples to supplement the article Turing machine.
A Turing machine is a hypothetical computing device, first conceived by Alan Turing in 1936. Turing machines manipulate symbols on a potentially infinite strip of tape according to a finite table of rules, and they provide the theoretical underpinnings for the notion of a computer algorithm.
The following article is a supplement to the article Turing machine.
Algorithm characterizations are attempts to formalize the word algorithm. Algorithm does not have a generally accepted formal definition. Researchers are actively working on this problem. This article will present some of the "characterizations" of the notion of "algorithm" in more detail.
In theoretical computer science the random-access stored-program (RASP) machine model is an abstract machine used for the purposes of algorithm development and algorithm complexity theory.
A counter machine is an abstract machine used in a formal logic and theoretical computer science to model computation. It is the most primitive of the four types of register machines. A counter machine comprises a set of one or more unbounded registers, each of which can hold a single non-negative integer, and a list of arithmetic and control instructions for the machine to follow. The counter machine is typically used in the process of designing parallel algorithms in relation to the mutual exclusion principle. When used in this manner, the counter machine is used to model the discrete time-steps of a computational system in relation to memory accesses. By modeling computations in relation to the memory accesses for each respective computational step, parallel algorithms may be designed in such a matter to avoid interlocking, the simultaneous writing operation by two threads to the same memory address.
Although some authors use the name "register machine" synonymously with "counter machine", this article will give details and examples of only of the most primitive species – the "counter machine" – of the genus "register machine."
In his book A New Kind of Science, Stephen Wolfram described a universal 2-state 5-symbol Turing machine, and conjectured that a particular 2-state 3-symbol Turing machine might be universal as well.
