How do you prove a TM is undecidable?
For a correct proof, need a convincing argument that the TM always eventually accepts or rejects any input. How can you prove a language is undecidable? To prove a language is undecidable, need to show there is no Turing Machine that can decide the language. This is hard: requires reasoning about all possible TMs.
How do you prove something is a Turing machine?
The standard way of proving something turing complete is to implement one of the TM-equivalents in your machine. If that is possible to do, then your machine is turing-complete. If it’s not, then it’s not.
What is Undecidable Turing machine?
A problem is undecidable if there is no Turing machine which will always halt in finite amount of time to give answer as ‘yes’ or ‘no’. An undecidable problem has no algorithm to determine the answer for a given input.
Why is ATM not decidable?
Because we know that ATM is recognizable, our theorem implies that ATM and ATM are both decidable. But we know that ATM is not decidable. This is a contradiction, hence ATM cannot be recognizable. The language ATM and its undecidability (including proof).
What makes a problem undecidable?
In computability theory, an undecidable problem is a type of computational problem that requires a yes/no answer, but where there cannot possibly be any computer program that always gives the correct answer; that is, any possible program would sometimes give the wrong answer or run forever without giving any answer.
How do you prove Turing completeness?
To prove that a language or device is Turing Complete all you have to do is show that it can be used to implement a Universal Turing machine. A language that has a default flow of control, conditional execution and repetition is Turing Complete with only minor additional requirements.
Are undecidable statements true?
In 1977, Paris and Harrington proved that the Paris-Harrington principle, a version of the Ramsey theorem, is undecidable in the axiomatization of arithmetic given by the Peano axioms but can be proven to be true in the larger system of second-order arithmetic.
Are undecidable problems unsolvable?
An undecidable problem is one for which no algorithm can ever be written that will always give a correct true/false decision for every input value. Undecidable problems are a subcategory of unsolvable problems that include only problems that should have a yes/no answer (such as: does my code have a bug?).
Why is ETM Undecidable?
ETM is not Turing-recognizable. Rice’s Theorem: Every nontrivial property of the Turing-recognizable languages is undecidable. regarded as a collection of dominos, each containing two strings, with one stacked on top of the other.)
How do you show that something is not Turing recognizable?
To prove that a given language is non-Turing-recognizable: Either do both of these: • Prove that its complement is Turing-recognizable. Prove that its complement is undecidable.
What is an undecidable problem example?
Examples – These are few important Undecidable Problems: Whether a CFG generates all the strings or not? As a CFG generates infinite strings, we can’t ever reach up to the last string and hence it is Undecidable. Since we cannot determine all the strings of any CFG, we can predict that two CFG are equal or not.
What is undecidable problem give example?
Example: the halting problem in computability theory Alan Turing proved in 1936 that a general algorithm running on a Turing machine that solves the halting problem for all possible program-input pairs necessarily cannot exist. Hence, the halting problem is undecidable for Turing machines.
How to solve the undecidable problem of the Turing machine?
If P1 is undecidable, then P2 is also undecidable. If P1 is non-RE, then P2 is also non-RE. Consider an instance w of P1. Then construct an algorithm such that the algorithm takes instance w as input and converts it into another instance x of P2. Then apply that algorithm to check whether x is in P2.
What’s the difference between a DFA and a Turing machine?
One difference from DFA or CFG is that the input for the Turing machine is actually on the tape: initially the tape contains only the input string and is blank everywhere else. When the machine starts, it will move around its states, tape head, and write content on the tape according to the transition function.
How did Alan Turing come up with his proof?
To do this perhaps it would use “heuristics” (tricks: taught or learned). For purposes of the proof, these details are not important. Turing then describes (rather loosely) the algorithm (method) to be followed by a machine he calls H. Machine H contains within it the decision-machine D (thus D is a “subroutine” of H).
What’s the difference between a Turing machine and a CFG?
There is a tape head that can read and write symbols and move around on the tape. One difference from DFA or CFG is that the input for the Turing machine is actually on the tape: initially the tape contains only the input string and is blank everywhere else.