Primjeri korištenja Turing machine na Engleski i njihovi prijevodi na Hrvatskom
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Contrast this to recursive languages, which require that the Turing machine halts in all cases.
Attempts to amend the definition of a Turing machine to produce a more powerful machine have surprisingly met with failure.
Computationally, a context-sensitive language is equivalent with a linear bounded nondeterministic Turing machine.
While each of them can solve the halting problem for a Turing machine, they cannot solve their own version of the halting problem.
A linear bounded automaton is a device which is more powerful than a pushdown automaton butless so than a Turing machine.
For example, the Turing machine may have a"halting oracle" which answers immediately whether a given Turing machine will ever halt on a given input.
The Church-Turing thesis conjectures that there is no effective model of computing that can compute more mathematical functions than a Turing machine.
The Turing machine then does the following: Start at the left of the second tape and repeatedly choose to move right or select the current position on the tape.
It can be shown(See main article: Halting problem)that it is not possible to construct a Turing machine that can answer this question in all cases.
The language consisting of all Turing machine descriptions paired with all possible input streams on which those Turing machines will eventually halt, is not recursive.
A reduction can be demonstrated to this problem from the well-known undecidable problem of determining whether a Turing machine accepts a particular input the halting problem.
Is it possible to change the definition of a Turing machine so that a particular class of total Turing machines, computing all the total computable functions, can be found?
This is the same as saying that for every unrestricted grammar G{\displaystyle G}there exists some Turing machine capable of recognizing L( G){\displaystyle L(G)} and vice versa.
Because Turing machines have the ability to"back up" in their input tape,it is possible for a Turing machine to run for a long time in a way that is not possible with the other computation models previously described.
A recursively enumerable language is a formal language for which there exists a Turing machine(or other computable function) which will enumerate all valid strings of the language.
Turing machine Also similar to the finite state machine, except that the input is provided on an execution"tape", which the Turing machine can read from, write to, or move back and forth past its read/write"head.
Here we are asking not a simple question about a prime number or a palindrome, butwe are instead turning the tables and asking a Turing machine to answer a question about another Turing machine. .
A recursive language is a formal language for which there exists a Turing machine that, when presented with any finite input string, halts and accept if the string is in the language, and halts and rejects otherwise.
Build a Turing machine M, using Kleene's recursion theorem, which on input 0 simulates the machine with index e running on an index nM for M thus the machine M can produce an index of itself; this is the role of the recursion theorem.
In particular, the partial function f defined so that f(n)m if and only if the Turing machine with index n halts on input 0 with output m has no extension to a total computable function.
Computer scientists study the Turing machine because it is simple to formulate, can be analyzed and used to prove results, and because it represents what many consider the most powerful possible"reasonable" model of computation see Church-Turing thesis.
A language can be given as those strings generated by some formal grammar; those strings described or matched by a particular regular expression;those strings accepted by some automaton, such as a Turing machine or finite state automaton; those strings for which some decision procedure(an algorithm that asks a sequence of related YES/NO questions) produces the answer YES.
For example, adding an extra tape to the Turing machine, giving it a two-dimensional(or three- or any-dimensional) infinite surface to work with can all be simulated by a Turing machine with the basic one-dimensional tape.
The halting problemis easy to solve, however, if we allow that the Turing machine that decides it may run forever when given input which is a representation of a Turing machine that does not itself halt.
It is easy to see that this Turing machine will generate all and only the sentential forms of G{\displaystyle G} on its second tape after the last step is executed an arbitrary number of times, thus the language L( G){\displaystyle L(G)} must be recursively enumerable.
To see that this language is not recursively enumerable,imagine that we construct a Turing machine M which is able to give a definite answer for all such Turing machines, but that it may run forever on any Turing machine that does eventually halt.
We can then construct another Turing machine M′{\displaystyle M'} that simulates the operation of this machine, along with simulating directly the execution of the machine given in the input as well, by interleaving the execution of the two programs.
Third part represents introduction to philosophy of logic. Turing machine, Markov algoritm and application of logic in linguistics and cognitive science, Russel-Whitehead 's reduction attempt, and Gödel 's uncertainty theorem.
An LBA differs from a Turing machine in that while the tape is initially considered to have unbounded length, only a finite contiguous portion of the tape, whose length is a linear function of the length of the initial input, can be accessed by the read/write head; hence the name linear bounded automaton.
The statement that the halting problem cannot be solved by a Turing machine is one of the most important results in computability theory, as it is an example of a concrete problem that is both easy to formulate andimpossible to solve using a Turing machine.