nondeterministic Turing Machine - Definition. Was ist nondeterministic Turing Machine
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Was (wer) ist nondeterministic Turing Machine - definition

MAY HAVE A SET OF RULES THAT PRESCRIBES MORE THAN ONE ACTION FOR A GIVEN SITUATION; STATE AND TAPE SYMBOL NO LONGER UNIQUELY SPECIFY THINGS; RATHER, MANY DIFFERENT ACTIONS MAY APPLY FOR THE SAME COMBINATION OF STATE AND SYMBOL
Non-deterministic Turing machine; NDTM; Nondeterministic Turing machines; Nondeterministic turing machine; Non-deterministic turing machine; Nondeterministic model of computation; Non deterministic Turing machine
  • solvable by quantum computers in polynomial time]] (BQP). Note that the figure suggests <math>\mathsf P \neq \mathsf{NP}</math> and <math>\mathsf{NP} \neq \mathsf{PSPACE}</math>. If this is not true then the figure should look different.

Nondeterministic Turing Machine         
<complexity> A normal (deterministic) Turing Machine that has a "guessing head" - a write-only head that writes a guess at a solution on the tape first, based on some arbitrary internal algorithm. The regular Turing Machine then runs and returns "yes" or "no" to indicate whether the solution is correct. A nondeterministic Turing Machine can solve nondeterministic polynomial time computational {decision problems} in a number of steps that is a polynomial function of the size of the input (1995-04-27)
Nondeterministic Turing machine         
In theoretical computer science, a nondeterministic Turing machine (NTM) is a theoretical model of computation whose governing rules specify more than one possible action when in some given situations. That is, an NTM's next state is not completely determined by its action and the current symbol it sees, unlike a deterministic Turing machine.
Turing Machine         
  • 3-state Busy Beaver. Black icons represent location and state of head; square colors represent 1s (orange) and 0s (white); time progresses vertically from the top until the '''HALT''' state at the bottom.
  • A Turing machine realization using [[Lego]] pieces
  • An implementation of a Turing machine
  • The evolution of the busy beaver's computation starts at the top and proceeds to the bottom.
  • finite-state representation]]. Each circle represents a "state" of the table—an "m-configuration" or "instruction". "Direction" of a state ''transition'' is shown by an arrow. The label (e.g. ''0/P,R'') near the outgoing state (at the "tail" of the arrow) specifies the scanned symbol that causes a particular transition (e.g. ''0'') followed by a slash ''/'', followed by the subsequent "behaviors" of the machine, e.g. "''P'' ''print''" then move tape "''R'' ''right''". No general accepted format exists. The convention shown is after McClusky (1965), Booth (1967), Hill, and Peterson (1974).
  • The head is always over a particular square of the tape; only a finite stretch of squares is shown. The instruction to be performed (q<sub>4</sub>) is shown over the scanned square. (Drawing after Kleene (1952) p. 375.)
  • Here, the internal state (q<sub>1</sub>) is shown inside the head, and the illustration describes the tape as being infinite and pre-filled with "0", the symbol serving as blank. The system's full state (its "complete configuration") consists of the internal state, any non-blank symbols on the tape (in this illustration "11B"), and the position of the head relative to those symbols including blanks, i.e. "011B". (Drawing after Minsky (1967) p. 121.)
  • Another Turing machine realization
ABSTRACT COMPUTATION MODEL; MATHEMATICAL MODEL OF COMPUTATION THAT DEFINES AN ABSTRACT MACHINE WHICH MANIPULATES SYMBOLS ON A STRIP OF TAPE ACCORDING TO A TABLE OF RULES
Turing Machine; Turing Machine simulator; Universal computation; Turing machines; Deterministic Turing machine; Universal computer; K-string Turing machine with input and output; Turing Machines; The Turing Machine; Universal computing machine; Turing-computable function; Turing table; A-machine
<computability> A hypothetical machine defined in 1935-6 by Alan Turing and used for computability theory proofs. It consists of an infinitely long "tape" with symbols (chosen from some finite set) written at regular intervals. A pointer marks the current position and the machine is in one of a finite set of "internal states". At each step the machine reads the symbol at the current position on the tape. For each combination of current state and symbol read, a program specifies the new state and either a symbol to write to the tape or a direction to move the pointer (left or right) or to halt. In an alternative scheme, the machine writes a symbol to the tape *and* moves at each step. This can be encoded as a write state followed by a move state for the write-or-move machine. If the write-and-move machine is also given a distance to move then it can emulate an write-or-move program by using states with a distance of zero. A further variation is whether halting is an action like writing or moving or whether it is a special state. [What was Turing's original definition?] Without loss of generality, the symbol set can be limited to just "0" and "1" and the machine can be restricted to start on the leftmost 1 of the leftmost string of 1s with strings of 1s being separated by a single 0. The tape may be infinite in one direction only, with the understanding that the machine will halt if it tries to move off the other end. All computer instruction sets, high level languages and computer architectures, including parallel processors, can be shown to be equivalent to a Turing Machine and thus equivalent to each other in the sense that any problem that one can solve, any other can solve given sufficient time and memory. Turing generalised the idea of the Turing Machine to a "Universal Turing Machine" which was programmed to read instructions, as well as data, off the tape, thus giving rise to the idea of a general-purpose programmable computing device. This idea still exists in modern computer design with low level microcode which directs the reading and decoding of higher level machine code instructions. A busy beaver is one kind of Turing Machine program. Dr. Hava Siegelmann of Technion reported in Science of 28 Apr 1995 that she has found a mathematically rigorous class of machines, based on ideas from chaos theory and {neural networks}, that are more powerful than Turing Machines. Sir Roger Penrose of Oxford University has argued that the brain can compute things that a Turing Machine cannot, which would mean that it would be impossible to create {artificial intelligence}. Dr. Siegelmann's work suggests that this is true only for conventional computers and may not cover {neural networks}. See also Turing tar-pit, finite state machine. (1995-05-10)

Wikipedia

Nondeterministic Turing machine

In theoretical computer science, a nondeterministic Turing machine (NTM) is a theoretical model of computation whose governing rules specify more than one possible action when in some given situations. That is, an NTM's next state is not completely determined by its action and the current symbol it sees, unlike a deterministic Turing machine.

NTMs are sometimes used in thought experiments to examine the abilities and limits of computers. One of the most important open problems in theoretical computer science is the P versus NP problem, which (among other equivalent formulations) concerns the question of how difficult it is to simulate nondeterministic computation with a deterministic computer.