HALT is not decidable (undecidable) Proof will involve the following Suppose there's some TM H that decides HALT Using this we will get a contradiction
slides
you should be able to ▷ Explain decidability, undecidability and the halting problem 3 and reductions ▷ Undecidability and semi-decidability 4 To show a problem decidable: write a program to solve it, prove the program terminates
itcs slides
A problem P is semi-decidable, if P is recursively enumerable There exists a 0 otherwise If the halting problem were decidable, then h were computable
limits
Semi-decidable • ATM and HTM both semi-decidable using UTM • Show HTM not decidable • Let E be candidate TM to decide HTM Show can't be right
Lecture
Hence, L1 is not semi-decidable An important natural language is the “blank tape halting problem” Define HB = {〈M〉Mis a Turing machine and
comp
9 mai 2016 · D6 Decidability and Semi-Decidability D7 Halting Problem and Reductions D8 Rice's Theorem and Other Undecidable Problems
theory d
18 oct 2017 · The ε-Halting Problem: recognise TMs that halt on the empty input Many further Theorem 4 5: The Halting Problem is semi-decidable
CT Lecture print
A language L is Turing-acceptable if and only if L is semi-decidable Petersen Balogh (HHU) Halting problem and Universal Turing machine Halting problem
ESSLLI FLT DAY
is well known that the complement of the halting problem for Turing machines is not semi-decidable The bulk of the proof has already been done: It is a well
decidability
{ (M,w) M is a TM that halts on string w } Theorem: HALT TM is undecidable THE classical HALTING PROBLEM Proof: Assume, for a contradiction, that TM H
Lecture .
Let Limpossible be some problem that we already know is undecidable (e.g. Halting). Proof by contradiction: Assume that there were some TM ML that decides L.
May 9 2016 Theorem (Semi-Decidability of the Special Halting Problem). The special halting problem is semi-decidable. Proof. We construct an ...
Theorem: the restricted halting problem RHP is not decidable. RHP := {〈M〉
Oct 18 2017 ... semi-decidable. We have seen examples for both: Theorem 4.5: The Halting Problem is semi-decidable. Proof: Use the universal TM to simulate ...
Apr 17 2019 Note: H is semi-decidable. (Why?) Theorem (Undecidability of General Halting Problem). The general halting problem is undecidable. Intuition ...
we'll ignore it when take complements etc.
May 11 2016 undecidable but semi-decidable problems: special halting problem a.k.a. self-application problem. (from previous chapter) general halting ...
Apr 28 2020 Deciding P is called the Halting Problem. We will write HALT to mean ... HALT is semi-decidable. Proof: Here is a semi-decision procedure for ...
The special halting problem is semi-decidable because we can construct a TM which semi-decides it as follows: If the input is not a valid coding of a TM the
Any semi-decidable problem P is computably enumerable. Why? Any computably Recall that Uniform Halting is the undecidable problem that contains all RM ...
Theorem: the restricted halting problem RHP is not decidable. RHP := {?M?
The Halting Problem. Theorem. HALT is not decidable (undecidable). Proof will involve the following. Suppose there's some TM H that decides. HALT.
we'll ignore it when take complements etc.
May 9 2016 D7. Halting Problem and Reductions. D8. Rice's Theorem and Other Undecidable Problems ... The special halting problem is semi-decidable.
Oct 18 2017 The ?-Halting Problem: recognise TMs that halt on the empty input ... Theorem 4.5: The Halting Problem is semi-decidable.
Unsolvability/Undecidability of the Halting Problem Semi-Decidable & Non-Semi-Decidable Languages ... Are there still problems we cannot solve?
Theorem: the non-acceptance problem NAP and the non-halting problem NHP are not semi-decidable Proof: if both a problem and its complement were semi-decidable
The Halting Problem Theorem HALT is not decidable (undecidable) Proof will involve the following Suppose there's some TM H that decides HALT
9 mai 2016 · Theorem (Semi-Decidability of the Special Halting Problem) The special halting problem is semi-decidable Proof We construct an “interpreter”
ATM and HTM both semi-decidable using UTM • Show HTM not decidable • Let E be candidate TM to decide HTM Show can't be right
Definition A problem (DQ) is semi-decidable if there is a TM/RM that returns “yes” for any d ? Q but may return “no” or loop forever when d /? Q
solvable must be incorrect Halting problem undecidable or semi decidable? Halting problem is undecidable but that does not make the problem semi-
A language L is Turing-acceptable if and only if L is semi-decidable Halting problem and Universal Turing machine Halting problem
18 oct 2017 · We have seen examples for both: Theorem 4 5: The Halting Problem is semi-decidable Proof: Use the universal TM to simulate an input TM and
HP = {?Mw?M is a TM and it does not halt on string w} 2 I use “decidable” and “recursive” interchangeably and use “semi-decidable” and “recursively
8 déc 2009 · The Halting Problem and Every TM for a semi-decidable+ language halts All semi-decidable+ languages are undecidable
Theorem: the non-acceptance problem NAP and the non-halting problem NHP are not semi-decidable. Proof: if both a problem and its complement were semi-decidable, Questions d'autres utilisateurs
Is the halting problem semi-decidable?
The halting problem and the acceptance problem are “equivalent”. Theorem: the halting problem HP is semi-decidable. Proof: we construct Turing machine M which takes (?M?,w) and simulates the execution of M on input w. If (the simulation of) M halts, M accepts its input.Is semi-decidable decidable?
Every decidable theory or logical system is semidecidable, but in general the converse is not true; a theory is decidable if and only if both it and its complement are semi-decidable. For example, the set of logical validities V of first-order logic is semi-decidable, but not decidable.What is a semi-decidable problem?
Definition. A problem (D,Q) is semi-decidable if there is a TM/RM that returns “yes” for any d ? Q, but may return “no” or loop forever when d /? Q. Semi-decidable problems are sometimes called recognisable.- The halting problem is partially computable
(p, x) ? HALT.
Decidable and Semi-decidable