What is an example of the halting problem?
For example, it’s easy to write a program that loops through ever-increasing values of a, b, c and n, and halts if it finds values such that a^n + b^n = c^n for n > 2. This program will halt if Fermat’s Last Theorem is false and will run forever if it’s true.
Can the halting problem ever be solved?
Halting problem is perhaps the most well-known problem that has been proven to be undecidable; that is, there is no program that can solve the halting problem for general enough computer programs.
Why is the halting problem undecidable?
This is an undecidable problem because we cannot have an algorithm which will tell us whether a given program will halt or not in a generalized way i.e by having specific program/algorithm.In general we can’t always know that’s why we can’t have a general algorithm.
What is the halting problem simple?
unsolvable algorithmic problem is the halting problem, which states that no program can be written that can predict whether or not any other program halts after a finite number of steps. The unsolvability of the halting problem has immediate practical bearing on software development.
Is Boolean satisfiability problem unsolvable?
As a consequence, for each CNF formula, it is possible to solve the XOR-3-SAT problem defined by the formula, and based on the result infer either that the 3-SAT problem is solvable or that the 1-in-3-SAT problem is unsolvable.
Can you solve sums on computer?
Answer: yes, computer can solve sum.
What is Rice theorem in TOC?
Rice theorem states that any non-trivial semantic property of a language which is recognized by a Turing machine is undecidable. A property, P, is the language of all Turing machines that satisfy that property.
What is halting problem in TOC?
The Halting Problem is the problem of deciding or concluding based on a given arbitrary computer program and its input, whether that program will stop executing or run-in an infinite loop for the given input.
What is an example of an undecidable problem?
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.
Is the halting problem a paradox?
In [1] the halting problem is compared to the Barber’s paradox. “The barber, who is a man, shaves all and only the men in the village who do not shave themselves. Who shaves the barber?” If we assume he shaves himself, we see we must be wrong, because the barber shaves only men who do not shave themselves.
What is the significance of the halting problem?
The Halting problem lets us reason about the relative difficulty of algorithms. It lets us know that, there are some algorithms that don’t exist, that sometimes, all we can do is guess at a problem, and never know if we’ve solved it.
Which of the problems are unsolvable halting problem?
One of well known unsolvable problems is the halting problem. It asks the following question: Given an arbitrary Turing machine M over alphabet = { a , b } , and an arbitrary string w over , does M halt when it is given w as an input? It can be shown that the halting problem is not decidable, hence unsolvable.