# Questions tagged [turing-machines]

Questions about Turing machines, a theoretical model of mechanical computation capable of simulating any computer program.

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### Is the two-color leapfrog problem in P?

My question is whether a specific decision problem is in P or not. It's straightforwardly in NP. The decision problem is a specific case of the general $k$-color leapfrog problem. I can already show ...
821 views

### Universal Turing Machine simulation with bounded time overhead

Is it possible to design a Universal Turing Machine in which the simulation time of a given Turing Machine $M$ is bounded by a factor of $\mathcal{O}(\log|\Gamma|+\log|Q|)$ of the original running-...
908 views

### Complexity of Sorting Integers on a Multitape Turing Machine

How expensive is sorting integers on a Multitape Turing Machine? Well known sorting algorithms, like quicksort, tend to rely on jumping / indirect-access being cheap. But MTMs have no indirect access.....
1k views

### Compiler that compiles to a Turing machine?

I am interested in finding/writing a compiler that compiles a program written in a simple source language to a Turing machine (instead of assembly). Does anyone know if there is a good approach for ...
33 views

### Unbounded-time programs in lambda calculus?

The Turing machine model has been extended to “infinitary turing machines”, which are Turing machines that can perform a countably and uncountably infinite amount of computations in finite time. Is ...
72 views

### Can all computational complexity results be expressed in terms of programming languages?

Computational complexity results are often explained in intuitive terms as statements about the possible efficiencies of algorithms to solve certain classes of problems. However, on a more formal ...
54 views

### What is the minimum acceleration of a macro machine?

In the context of Turing machines, consider a $k$-sized macro machine (k-MM) which operates on groups of $k$ symbols at once. This is a common optimization in the search for Busy Beavers, explained e....
182 views

### 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 ...
2k views

### Prove that turing machines and the lambda calculus are equivalent

It is known that a turing machine and the lambda calculus are equivalent in power. I now want to try to prove this myself. I think proving that the lambda calculus is at least as powerful as a turing ...
99 views

### How to model reversible interactive programs

Reversible programs with finite execution steps are well studied. For example, a Turing machine whose transitions are reversible and halts can be executed backwards consuming its tape in the reverse ...
132 views

### Is a reduced Wang B-machine Turing-complete?

A Wang B-machine has only 4 instructions: right: Move tape head right left: Move tape head left ...