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# Similar reasoning shows that no program that is substantially shorter than N bits long can solve the Turing halting problem for all programs up to N bits long.<ref name="ref_af436557">[https://www.scientificamerican.com/article/why-is-turings-halting-pr/ Why is Turing's halting problem unsolvable?]</ref>
 
# Similar reasoning shows that no program that is substantially shorter than N bits long can solve the Turing halting problem for all programs up to N bits long.<ref name="ref_af436557">[https://www.scientificamerican.com/article/why-is-turings-halting-pr/ Why is Turing's halting problem unsolvable?]</ref>

2021년 2월 25일 (목) 23:02 기준 최신판

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  1. Similar reasoning shows that no program that is substantially shorter than N bits long can solve the Turing halting problem for all programs up to N bits long.[1]
  2. Back when I was a PhD student, I needed a succinct way to sunmarize the Halting Problem, one of the core demonstrations of the limits of computation.[2]
  3. and I managed to write a solution to the halting problem.[2]
  4. I claimed that would_it_stop was a solution to the halting problem.[2]
  5. It turns out that these sorts of problems are all equivalent to the halting problem, in the sense that given a solution to one of them, you could write a solution to any of the other ones.[2]
  6. A key part of the proof is a mathematical definition of a computer and program, which is known as a Turing machine; the halting problem is undecidable over Turing machines.[3]
  7. The difficulty in the halting problem lies in the requirement that the decision procedure must work for all programs and inputs.[3]
  8. The halting problem is theoretically decidable for linear bounded automata (LBAs) or deterministic machines with finite memory.[3]
  9. The halting problem is historically important because it was one of the first problems to be proved undecidable.[3]
  10. How would you describe Turing's Halting Problem to a 13-year-old?[4]
  11. How would the proof for the halting problem help us with the Entscheidungsproblem?[5]
  12. Let us now apply Cantor’s Diagonal Argument to the halting problem.[5]
  13. To get an appreciation of why this is the case, put on your thinking caps and we’ll discuss some of the ideas behind compatibility and the halting problem in an informally rigorous way.[6]
  14. The setup of the halting problem is as such that it leads to a contradiction; let’s define a halting set H as a set of all programs or algorithms that halt on some arbitrary inputs.[6]
  15. The implications of the halting problem are certainly remarkable.[6]
  16. Conceivably we can build a meta-system to see if a subsystem of halt checkers runs into the halting problem.[6]
  17. Alternatively, if A is prime and decidable, then again the embedding problem into decidable models can only be as complex as the Halting Problem, although for a different reason.[7]
  18. The halting problem is solvable for machines with less than four states.[8]
  19. The Halting Problem is one of the simplest problems know to be unsolvable.[9]
  20. We will consider the halting problem to demonstrate this claim and to show that, in fact, many interesting questions about programs are undecidable.[10]
  21. While we will not refer to the proof of the halting problem’s undecidability in the rest of the course, understanding it is very useful for a computer scientists.[10]
  22. (written in your favorite programming language) that solves the halting problem.[10]
  23. would halt if run, we have a solution to the halting problem.[10]
  24. The proof is close to the proof given by Turing in 1936 of the undecidability of the Halting problem.[11]
  25. We also give an activity to prove the undecidability of the Halting problem.[11]
  26. The halting problem for Turing machines is decidable on a set of asymptotic probability one.[12]
  27. No algorithm can of course solve the Halting Problem, that is, decide within finite time always correctly whether a given program halts on a certain given input.[13]
  28. Hilbert played the same role regarding Alan Turing’s proof of the halting problem.[14]
  29. Here it is possible to see how the Halting Problem is related to Gödel’s Incompleteness Theorem.[14]
  30. The halting problem proves that there is more to cognition than computation.[14]
  31. Since the halting problem is not solved even by an infinite amount of information, it will apply to the Demon too.[14]
  32. In this paper we propose and study an efficient statistical anytime algorithm for the Halting Problem.[15]
  33. The Halting Problem asks to decide, from a description of an arbitrary program and an input, whether the computation of the program on that input will eventually stop or continue forever.[15]
  34. In 1936 A. Church, and independently A. Turing, proved that there is no algorithm solving the Halting Problem for all possible program-input pairs.[15]
  35. The Halting Problem has many applications in logic and theoretical as well as applied computer science, mathematics, physics, biology, etc.[15]
  36. halts, we have constructed a solution to the halting problem.[16]
  37. Example: The halting problem is partially computable.[16]
  38. If the halting problem HALTS(P,D) halts and says Yes, it is easy to check that P(D) halts by showing a simulation of P(D).[16]
  39. It is shown that the halting problem for the class of 2-state Post machines is solvable.[17]
  40. The algorithm can be naturally programmed as a faster hybrid classical-quantum algorithm for classes of instances of the Halting Problem.[18]
  41. Halting problem program goes -- here.[19]
  42. tests whether the program represented by halts when given th e as input (using the Halting Problem procedure, , to perform the test).[19]

소스

  1. ↑ Why is Turing's halting problem unsolvable?
  2. ↑ 2.0 2.1 2.2 2.3 The Craig Web Experience · The Halting Problem
  3. ↑ 3.0 3.1 3.2 3.3 Halting problem
  4. ↑ How to Describe Alan Turing's Halting Problem to a 13 Year Old
  5. ↑ 5.0 5.1 Why Would You Care About the Halting Problem?
  6. ↑ 6.0 6.1 6.2 6.3 A Crash course on proving the Halting Problem
  7. ↑ Halting Problem - an overview
  8. ↑ Halting Problem -- from Wolfram MathWorld
  9. ↑ The Halting Problem
  10. ↑ 10.0 10.1 10.2 10.3 CS 251: Computability and the Halting Problem
  11. ↑ 11.0 11.1 How to Teach the Undecidability of Malware Detection Problem and Halting Problem
  12. ↑ Hamkins , Miasnikov : The Halting Problem Is Decidable on a Set of Asymptotic Probability One
  13. ↑ On Approximating Real-World Halting Problems
  14. ↑ 14.0 14.1 14.2 14.3 The Halting Problem
  15. ↑ 15.0 15.1 15.2 15.3 A statistical anytime algorithm for the Halting Problem
  16. ↑ 16.0 16.1 16.2 Formal Computational Models and Computability
  17. ↑ The Solvability of the Halting Problem for 2-State Post Machines
  18. ↑ A Statistical Anytime Algorithm for the Halting Problem
  19. ↑ 19.0 19.1 Computability and Complexity

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