# Questions tagged [halting-problem]

Questions concerning the Halting problem which is to decide whether a given a program halts on a given input.

28 questions with no upvoted or accepted answers
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### Difficulty in the halting problem for a simple Turing machine with standard enumerations of programs and of initial tape configurations

Preparations Consider a Turing machine with just one head and one tape (on which the head may move left, move right, or remain stationary), and with just two symbols ("blank" and "non-blank"). The ...
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### Are Turing machines with a limited but exponential tape decidable?

The Halting problem for Turing machines which work on a tape of at most $k$ cells can be solved: There is a limited number of distinct configurations available, providing an upper bound of steps ...
68 views

### Detecting loops in NPDAs

I'm aware that the halting problem is solvable for PDAs, but I have recently discovered that I am wrong about how to actually do it. I used to think that you could detect an infinite loop by meeting ...
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### How to create model for a powerful language whose programs are guaranteed to terminate?

I'm creating a powerful regular expression matching system that can be augmented by adding small microprograms to deterministic finite automaton (DFA) states. The microprogram solves the big bang ...
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### Is there an impossibility to mechanically distinguish between sets and classes?

Assuming only computable functions, and in line with set theory, defining a "proper class" as a collection that is itself not allowed to be a member of a set. A "collection" is then defined as either ...
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### Prove that $H$ reduces to $H\varepsilon$

I have to prove that $H_\varepsilon = \{<M> \mid M\ \text{halts on input }\varepsilon\}$ reduces to $H$ (the halting problem). I am very confused how to PROVE it, I mean it is clear that we can ...
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### Computational models where halting problem is solvable

Are there computational models that can be considered useful for solving common programming problems, where it can be proven that computation will terminate for all possible inputs?
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### What portion of all possible turing machines halt?

Has anyone estimated Chaitin's constant for Turing machines with an empty tape as input?
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### Reducing Halting Problem to Acceptor for TM

We have $A_{TM}=\{(M,w)|M$ is a TM, $w\in \Sigma^*_{TM},M$ accepts $w\}$ We intend to show that $HALT(M,w)\leq_T A_{TM}$ i.e. if we are given a machine for $A_{TM}$, we can decide whether $M$ halts ...
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### Is there evidence to suggest Macsyma was directed at the Diophantine equations in the Entscheidungsproblem?

I'm reading the book The Annotated Turing by Charles Petzold. In it he mentions the Diophantine equations - which was a joy to read. This then lead to Hilbert's 10th problem - finding an algorithm ...
### Mapping reduction from $A_{TM}$ exercise
Let $L = \{\langle M \rangle \mid \text{M is a TM which accepts only the string "010"}\}$. Prove that $L$ is undecidable. This is my solution, reducing $A_{TM}$ to $L$: $R(\langle M,w \rangle)$ ...