Tagged Questions

Given a program and the input for it, does it halt or run forever?

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Halting problem for finite tape TM [closed]

If we have a primitive CPU/computer with small amount of registers and/or RAM, it is easy to check if the program will loop endlessly: just write down all registers/RAM cells states at each state and ...
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Is there a good notion of non-termination and halting proofs in type theory?

Constructive type theory with its basic interpretation under the curry howard correspondence consists only of total, computable functions. In the literature, some has been said on using "computational ...
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Constructive proof of the Halting Problem

Does there exist any constructive (indeed, computable) proof of the Halting Problem? All the ones I have encountered make use of proof by contradiction. As an aside, some proofs I have encountered ...
92 views

Polynomial-time reductions between undecidable languages

The Turing degree $\mathbf{0}'$ is defined as all languages Turing-equivalent to the halting problem. In fact any recursively enumerable language is polynomial-time reducible to the halting problem. ...
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The halting problem in computational models weaker than Turing machines

What are the main results and/or literature on the (self) halting problem for other machines than Turing machines? Alternatively, what would be the right keywords or tags to search for it. I am ...
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Undecidable Single Programs [closed]

So the halting problem basically states that there cannot exist any finite length algorithm for automatically verifying if other finite length algorithms terminate. But suppose I start listing out ...
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Is there value in a faster soultion for the Halting Problem in a Linear Bounded Automata?

Sorry for being so informal, but I was thinking a bit about how the Halting Problem is solvable on a LBA but very very slow, in that if you have gone though more states in execution then the total ...
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Are All Turing-Uncomputable Sets Isomorphic to the Halting Problem? [closed]

We know from computability theory that some sets are recursively computable on a Turing machine and others not. Many such sets or languages that cannot be recognized by a Turing machine seem to have ...
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Turing machines whose termination is unprovable?

I have a naive question: does there exist a Turing machine whose termination is true but unprovable by any natural, consistent and finitely axiomatizable theory? I ask for a mere existence proof ...
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What is the smallest Turing machine where it is unknown if it halts or not?

I know that the halting problem is undecidable in general but there are some Turing machines that obviously halt and some that obviously don't. Out of all possible turing machines what is the smallest ...
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Is refuting candidate deciders of the halting problem computable? [closed]

No Turing machine can decide whether any given Turing machine will halt for a given input. That is: If you give me a Turing machine which you claim can take a Turing machine and an input for that ...
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Is there a hidden link between the existence uncountable sets and the undecidability of the halting problem?

Since both proofs make use of the diagonal argument, I’m wondering whether there is an obscure link between the existence of uncountable infinite sets and the undecidability of the halting problem. ...
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Explanation of 1-generic to prove undecidability of halting problem

This question is about an answer in question Are there any proofs the undecidability of the halting problem that does not depend on self-referencing or diagonalization ? Bjørn Kjos-Hanssen ...
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Complexity of the halting problem

One of the most celebrated results in computer science is that the halting problem is undecidable. However there are still notions of complexity that are applicable. Here are 3 that I have in mind: \$...
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What is the “nearest” problem to the Collatz conjecture that has been successfully resolved?

I am interested in the "nearest" (and "most complex") problem to the Collatz conjecture that has been successfully solved (which Erdos famously said "mathematics is not yet ripe for such problems"). ...
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Halting problem, uncomputable sets: common mathematical proof?

It is known that with a countable set of algorithms (characterised by a Gödel number), we cannot compute (build a binary algorithm which checks belonging) all subsets of N. A proof could be ...
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Can every undecidability proof be converted into diagonalization proof? [duplicate]

Possible Duplicate: Are there any proofs the undecidability of the halting problem that does not depend on self-referencing or diagonalization ? As is stated, can every undecidability proof ...
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Is there any proof that a network made of Turing machines can't solve the halting problem? [closed]

My question points to the fact that Turing machines are isolated by definition. But what if they can send and receive information from/to other Turing machines? What if they can be "interrupted" at ...
553 views

Is halting that hard? [Yes] [closed]

I want to make a modification to the halting problem. The output now has two possibilities: This program halts and it does not have the crossing structure (defined below); This program does not halt ...
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Can chess simulate a Universal Turing Machine?

I am looking to get a definite answer to title question. Is there a set of rules that translates any program into a configuration of finite pieces on an infinite board, such that if black and white ...
717 views

Collatz Conjecture & Grammars / Automata

I was wondering if there is a good bibliography of attempts to investigate the Collatz conjecture as a formal grammar? (or any other attempts in the CS community to deal with this class of generative ...
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formalizing a statement about the expressive power of programming languages wrt divergence

In the Coq'Art book the authors mention in passing that any language that can calculate all computable functions must also be able to express diverging computations. Or in other words, there can be no ...
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Undecidable problems not Turing-complete?

are there systems whose nontrivial properties can't be decided by Turing machines, but for which a Turing machine with an oracle able to find out these properties isn't able to solve the Halting ...