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Each circle represents a "state" of the table—an "m-configuration" or "instruction". No general accepted format exists.

Usually large tables are better left as tables Booth, p. They are more readily simulated by computer in tabular form Booth, p. Hill and Peterson p. Whether a drawing represents an improvement on its table must be decided by the reader for the particular context.

See Finite state machine for more. The reader should again be cautioned that such diagrams represent a snapshot of their table frozen in time, not the course "trajectory" of a computation through time and space. While every time the busy beaver machine "runs" it will always follow the same state-trajectory, this is not true for the "copy" machine that can be provided with variable input "parameters".

On the far right is the Turing "complete configuration" Kleene "situation", Hopcroft—Ullman "instantaneous description" at each step. If the machine were to be stopped and cleared to blank both the "state register" and entire tape, these "configurations" could be used to rekindle a computation anywhere in its progress cf.

Turing The Undecidable, pp. Models equivalent to the Turing machine model[ edit ] See also: Turing machine equivalentsRegister machineand Post—Turing machine Many machines that might be thought to have more computational capability than a simple universal Turing machine can be shown to have no more power Hopcroft and Ullman p.

They might Ib history extended essay abstract faster, perhaps, or use less memory, or their instruction set might be smaller, but they cannot compute more powerfully i. Recall that the Church—Turing thesis hypothesizes this to be true for any kind of machine: A Turing machine is equivalent to a single-stack pushdown automaton PDA that has been made more flexible and concise by relaxing the last-in-first-out requirement of its stack.

In addition, a Turing machine is also equivalent to a two-stack PDA with standard last-in-first-out semantics, by using one stack to model the right side and the other stack to model the left side of the Turing machine.

At the other extreme, some very simple models turn out to be Turing-equivalenti. Common equivalent models are the multi-tape Turing machinemulti-track Turing machinemachines with input and output, and the non-deterministic Turing machine NDTM as opposed to the deterministic Turing machine DTM for which the action table has at most one entry for each combination of symbol and state.

For practical and didactical intentions the equivalent register machine can be used as a usual assembly programming language. An interesting question is whether the computation model represented by concrete programming languages is Turing equivalent. While the computation of a real computer is based on finite states and thus not capable to simulate a Turing machine, programming languages themselves do not necessarily have this limitation.

For example, ANSI C is not Turing-equivalent, as all instantiations of ANSI C different instantiations are possible as the standard deliberately leaves certain behaviour undefined for legacy reasons imply a finite-space memory.

This is because the size of memory reference data types is accessible inside the language. However, other programming languages like Pascal do not have this feature, which allows them to be Turing complete in principle.

It is just Turing complete in principle, as memory allocation in a programming language is allowed to fail, which means the programming language can be Turing complete when ignoring failed memory allocations, but the compiled programs executable on a real computer cannot.

Choice c-machines, oracle o-machines[ edit ] Early in his paper Turing makes a distinction between an "automatic machine"—its "motion When such a machine reaches one of these ambiguous configurations, it cannot go on until some arbitrary choice has been made by an external operator.

This would be the case if we were using machines to deal with axiomatic systems. He "suppose[s] that the choices are always between two possibilities 0 and 1.

Each proof will then be determined by a sequence of choices i1, i2, The automatic machine carries out successively proof 1, proof 2, proof 3, An oracle machine or o-machine is a Turing a-machine that pauses its computation at state "o" while, to complete its calculation, it "awaits the decision" of "the oracle"—an unspecified entity "apart from saying that it cannot be a machine" TuringThe Undecidable, p.

It is possible to invent a single machine which can be used to compute any computable sequence. If this machine U is supplied with the tape on the beginning of which is written the string of quintuples separated by semicolons of some computing machine M, then U will compute the same sequence as M.

This finding is now taken for granted, but at the time it was considered astonishing. The model of computation that Turing called his "universal machine"—"U" for short—is considered by some cf.

Davis to have been the fundamental theoretical breakthrough that led to the notion of the stored-program computer. This result was obtained in by F. Arora and Barak,theorem 1.

What is neglected in this statement is that, because a real machine can only have a finite number of configurations, this "real machine" is really nothing but a linear bounded automaton. On the other hand, Turing machines are equivalent to machines that have an unlimited amount of storage space for their computations.The norms for this feature are clearly stated by the IBO: “The requirements for the abstract are for it to state clearly the research question that was investigated, how the investigation was undertaken and the conclusion(s) of the essay.”.

The IB Extended Essay (or EE) is a 4, word structured mini-thesis that you write under the supervision of an advisor (an IB teacher at your school), which counts towards your IB Diploma (to learn about all of the IB diploma requirements, check out our other article).

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