Why can Conway’s Game of Life be classified as a universal machine?

I was recently reading about artificial life and came across the statement, “Conway’s Game of Life demonstrates enough complexity to be classified as a universal machine.” I only had a rough understanding of what a universal machine is, and Wikipedia only brought me as close to understanding as Wikipedia ever does. I wonder if anyone … Read more

What are the practical limitations of a non-turing complete language like Coq?

As there are non-Turing complete languages out there, and given I didn’t study Comp Sci at university, could someone explain something that a Turing-incomplete language (like Coq) cannot do? Or is the completeness/incompleteness of no real practical interest (i.e. does it not make much difference in practice)? EDIT – I’m looking for an answer along … Read more

Is the C99 preprocessor Turing complete?

After discovering the Boost preprocessor’s capabilities I found myself wondering: Is the C99 preprocessor Turing complete? If not, what does it lack to not qualify? Answer Well macros don’t directly expand recursively, but there are ways we can work around this. The easiest way of doing recursion in the preprocessor is to use a deferred … Read more

I’ve heard that LaTeX is Turing complete. Are there any programs written in LaTeX?

It’s possible to do interesting things with what would ordinarily be thought of as typesetting languages. For example, you can construct the Mandelbrot set using postscript. It is suggested in this MathOverflow question that LaTeX may be Turing-complete. This implies the ability to write arbitrary programs (although it may not be easy!). Does anyone know … Read more

C++ templates Turing-complete?

I’m told that the template system in C++ is Turing-complete at compile time. This is mentioned in this post and also on wikipedia. Can you provide a nontrivial example of a computation that exploits this property? Is this fact useful in practice? Answer I’ve done a turing machine in C++11. Features that C++11 adds are … Read more

What is Turing Complete?

What does the expression “Turing Complete” mean? Can you give a simple explanation, without going into too many theoretical details? Answer Here’s the briefest explanation: A Turing Complete system means a system in which a program can be written that will find an answer (although with no guarantees regarding runtime or memory). So, if somebody … Read more

If only using bit-shifts can produce a Turing-machine, or if you need more bitwise operations

So you can have One Instruction Set Computers. But typically these instructions have rather complicated underlying implementations. addition (addleq, add and branch if less than or equal to zero) decrement (DJN, decrement and branch (jump) if nonzero) increment (P1eq, plus 1 and branch if equal to another value) subtraction (subleq, subtract and branch if less … Read more

Is there a recursive problem encoding the Turing completeness of a model of computation?

Suppose we have a model of computation C we want to show to be Turing complete. The usual strategy would be to emulate within C any model of computation we already know to be Turing complete (e.g. an arbitrary Turing machine). On the other hand, a model of computation is Turing complete if and only … Read more

Turing-completeness of affine programs

Are unguarded affine programs Turing-Complete? Are affine programs with affine guards Turing-Complete? Unguarded program: all branches are taken Affine program: only assignments like x:=x1+5×2−x3+4(Affine equations as right hand) Affine guards: all conditional branches have only affine guards, for instance x1+x2−3×3>2 Answer AttributionSource : Link , Question Author : Linpeng Zhang , Answer Author : Community